Yes, it’s definitely possible to have successful ovulation and get pregnant without egg white cervical mucus. If you don’t experience the classic egg white cervical fluid at ovulation time, this doesn’t mean that you won’t get pregnant, it just means it can be a trickier journey for the sperm.
If you don’t see the egg white cervical fluid, it is especially important to confirm that you actually did ovulate by testing your progesterone levels 7 days after you experience ovulation pain and/or get a positive LH surge if you’re using OPK urine testing for LH levels.