Can a man with a big varicocele of the testicle still have children?

Sometimes yes: The connection of varicocele and male sub-fertility is not entirely consistent: though some men with sub-fertility are helped by varicocele repair, a majority of men with varicocele never have fertility problems. Expert groups of urologists and res often disagree on specifics, so for a less general answer i recommend getting a in-person evaluation with an expert you trust.

Yes: Fertility with a large varicocele is emininently possible, younger you are the better. Varicoceles increasingly affect sperm count with increasing age. Need to get a semen analysis if your spouse has difficulty conceiving. Could consider varicocelectony/spermatic vein ligation if sperm motility count low. Artificial insemination with your sperm or invitro-fertilization (ivf)are back-ups. Good luck.