It it's a "Navajo" type thickness (like less than 1/2 inch) it should be fine.
In fact, if the pad is thin, even folding it once should not be a problem. I kind of depends on how the English saddle fits. If it's a very close fit, then thick blankets worsen the fit. It it's on the wide side, then a thicker blanket is acceptable. Not that a really overly wide saddle is acceptable in the first place.