I don't recommend it. There's residue in the eggs however slight. It can extend the withdrawal period, but more importantly the residue can help build worm resistance to the product, so the next time you use it, it may or may not get rid of worms. It's best to toss the eggs in the garbage. A...
I forgot to add; once you dose her, keep an eye on her feces for the first 24 hours or so, you might see evidence of the tapeworm excreted. Tapeworms are flat and segmented, come in all shapes and sizes. They might look like a flat piece of macaroni or jellyfish like tentacles, or broken up...
Those are tapeworm segments. Your hen has tapeworms, now you know why she is sick...skin and bones. Safeguard will not kill tapeworms. Take the safeguard equine paste back where you got it from and swap it out for Zimectrin Gold equine paste. It will kill tapeworms. Here's a pic what it looks...
Not safeguard. Valbazen or zimectrin gold. Z-gold would be much cheaper, a pea size amount orally, then repeat again in 10 days. (If in fact it's tapes, OP isnt sure.)