More specifically, it actually is possible (I did achieve a level of success with this mechanism), but because of platform limitations, it's burdensome. You must two a two-step screen in order to successfully do this. Here's some snippets of data (this is a PayPal version):

// Step 1. We use Person Accounts in this example.
// Input: a bunch of parameters regarding contact information.
// Output: records ready to be processed by payment connect.
    Id recordTypeId = [select id from recordtype where ispersontype = true limit 1].Id;
    account a = new account(persontitle=title,firstname=firstname,lastname=lastname,
                personemail=email,personhasoptedoutofemail=(emailoptout=='1'||emailoptout=='true'),
                billingstreet=street,personmailingstreet=street,
                billingcity=city,personmailingcity=city,
                billingstate=state,personmailingstate=state,
                billingpostalcode=postalcode,personmailingpostalcode=postalcode,
                billingcountry=country,personmailingcountry=country,
                recordtypeid=recordtypeid);
    insert a;
Opportunity o = new opportunity(name='Web Payment',accountid=a.id,closedate=system.today(),stagename='Not Received',amount=amount);
    insert o;
                pymt__Processor_Connection__c pc = [select id from pymt__Processor_Connection__c  where RecordType.Name = 'PayPal' limit 1]; // Change this query.
pymt__PaymentX__c p = new pymt__PaymentX__c(pymt__contact__c=a.personcontactid,pymt__opportunity__c=o.id,name='Web Payment',pymt__processor_connection__c=pc.id);
    insert p;
    // (Store a.id, o.id, and p.id in controller, or even the entire object. Need this for step 2.)

// Step 2: On confirmation of details, like Site Checkout does, execute this code.
// Inputs: a bunch of credit card details, plus account, opportunity, and payment records.
// Output: none. Success is determined by a field, but since it is a asynchronous
//     request, we have to follow up later.
// IPAddress comes from "ipaddress = apexpages.currentpage().getheaders().get('X-Salesforce-SIP');"

            pymt.PayPalAPI.CustomerInfo cinfo = new pymt.PayPalAPI.customerinfo();
            pymt.PayPalAPI.shippinginfo sinfo = new pymt.PayPalAPI.shippinginfo();
            cinfo.firstname=a.firstname;
            cinfo.lastname=a.lastname;
            cinfo.email=a.personemail;
            cinfo.customerIP=ipaddress;
            sinfo.address=a.billingstreet;
            sinfo.city=a.billingcity;
            sinfo.state=a.billingstate;
            sinfo.postalcode=a.billingpostalcode;
            sinfo.country=a.billingcountry;
 pymt.PaymentX.TransactionResultExt result = pymt.PayPalConnector.chargeCreditCard('Payment Description',o.Amount,p.id,null,cinfo,sinfo,cardnumber,cardtype,expmonth+expyear,cvv,null,null,null,null,null,false);
        // result.pxSuccess == true means no problems with the attempt. Does not guarantee card is charged, only that paypal received the request.

This is their "Level 3" integration, and a total pain in the rear. The Recurring payments feature is even more burdensome, as you have to replace Step 2 with something like this:

// Inputs: Account, Opportunity, Payment, as before, plus credit card info.
// Output: Processed payment, as before.

map<string,string> paramMap = new map<string,string>();
      paramMap.put('METHOD','CreateRecurringPaymentsProfile');
      paramMap.put('SUBSCRIBERNAME',a.FirstName+' '+a.LastName);
      paramMap.put('PROFILESTARTDATE',string.valueof( datetime.newinstance( system.today().year(),system.today().month(),system.today().day())).replace(' ','T')+'.00Z');
      paramMap.put('DESC','Web Subscription');
      paramMap.put('BILLINGPERIOD',Period=='Year'?'Year':'Month');
      paramMap.put('BILLINGFREQUENCY',Period=='Quarter'?'3':'1');
      paramMap.put('AMT',String.valueOf(o.Amount.setScale(2)));
      paramMap.put('CURRENCYCODE','USD');
      paramMap.put('CREDITCARDTYPE',CardType);
      paramMap.put('ACCT',CardNumber);
      paramMap.put('EXPDATE',ExpMonth+ExpYear);
      paramMap.put('CVV2',CVV);
      paramMap.put('FIRSTNAME',a.FirstName);
      paramMap.put('LASTNAME',a.LastName);
      paramMap.put('STREET',a.BillingStreet);
      paramMap.put('CITY',a.BillingCity);
      paramMap.put('STATE',a.BillingState);
      paramMap.put('ZIP',a.BillingPostalCode);
      paramMap.put('COUNTRYCODE',a.BillingCountry);
      paramMap.put('CUSTOM','sfaccountid='+a.id+'&sfcontactid='+a.personcontactid+'&sfopportunityid='+o.id);
      string paramList = createNVP(paramMap);
      pymt.PayPalConnector.CreateRecurringPaymentsProfileResult result = pymt.PayPalConnector.createRecurringPaymentsProfile(pc.id, paramList);
        // result.resultCode=='Success' means all is well in the world.

createNVP is just a function that puts all the parameters into a NVP string as you'd do for PayPal directly.

Note that you don't need to store CVV, CreditCardNumber, ExpDate, or any other details anywhere in your system. Once handed to PayPal, you'll receive notifications through their Payment Relay of updates to your opportunities/payments/etc. You can use the fields they've provided to trigger workflow rules (such as emails), when the record is processed successfully. Note that additional fields may be required depending on your specific use case (i.e. if there is a trial fee, trial period, etc). Note that my subscription above is infinitely recurring; you can provide additional options to limit the number of times it processes, etc.

In either event, you'll need to create a page that does something like this:

<apex:page ...>
  <apex:outputText rendered="{!step1}"> Please give me your data </apex:outputText>
  <apex:outputText rendered="{!step2}"> Please confirm your data </apex:outputText>
  <apex:outputText rendered='{!step3}"> Thank you! </apex:outputText>
</apex:page>

After over a month of experimentation, costly consultation with Linvio, and so on, we basically found that you might as well use SiteCheckout and save yourself the hassle.