Can a landlord enter rental unit without notice if a "no pets" violation is suspected?

Generally, a landlord cannot enter an apartment without proper notice (and the amount of notice required is governed by local and/or state law) unless it is an emergency. I don't think this qualifies as an emergency.

If you think they have dogs, just knock on the door and you'll know soon enough if they have dogs. If you know the tenant is home at certain times of the day you could show up at that time unannounced and ask if they will let you inspect the apartment. They can refuse and then you have a decision to make.

You will find out the same way you found out they had pets in the first place. You will not see pets; you will not hear pets. If you don't see or hear these pets, they are probably gone.