I agree with Beth, if the holes are in a waterproof layer there isn't a lot you can do. But for a fitted, I say go for it, even just to prevent poo leaks while you get new diapers.
Do you have a sewing machine? If so, I've used a 3-step zig-zag to go back and forth over holes to mend them. Try to close the hole up as much as possible before you start.
To sew by hand, start at one end of the hole, insert your needle under or between the layers to hide the knot, bring it up and then start doing overcast stitches, bringing the two edges together.
For small, just starting holes, try dabbing on some Fraycheck or Frayblock, it won't mend the hole but it will keep it from getting bigger.