Can abnormal sperm fertilize an egg? would pregnancy continue normally if the fertilizing sperm was abnormal??

Depends: Hi. "Normal" and "abnormal" are points on a spectrum, with a continuum between them. So it depends how you define normal. Normal sperm (good viability, good swimmers) can hold a very bad allele that can cause really bad disease; would you call that a "normal" sperm since it fertilized the egg? If you define that sperm as abnormal because of the deleterious mutation, then yes, preg can continue.