Almost never. The only time you'll split 4's is when the dealer upcard is a 5 or a 6.
A pair of 4's is a hard total of 8, which gives you a good chance of catching an 18 for your finishing total, which is a reasonable hand.
If the dealer has a 5 or a 6, she has a great chance of busting. You're hoping to catch a couple of totals of 14 when you split, which will win if the dealer busts.