Joan Tudor / Williams

I know for certain that, like many others, I'm descended from Oliver Cromwell.
The question is 'Was Oliver Cromwell descended from Jasper Tudor through an illegitimate daughter, Joan, and on that basis descended from royalty via Owen Tudor and Catherine de Valois?
What evidence is there that Joan really existed or was she just a means that people at the time used for 'establishing' that Oliver Cromwell had royal connections, something that would have been advantageous to the cause when offering him the crown in the 1657?