If a tenant of an apartment willingly accepts a roommate, can the roomate be served with an order of protection or arrested for tresspassing?

The wording of your question is a bit confusing and does
not have enough facts to be able to definitively answer the question. What I can do is
explain how the law works in most states.

First, let us
look at the term "order of protection." An order of protection in most states is a court
order that is used to remove a person who is a family member, a spouse, or a boyfriend
or girlfriend, always a person who has abused or who has threatened to abuse.  I do not
know what state you reside in, but generally, a roommate is not a person who can be
removed pursuant to an order of protection.

Second,
usually, only a landlord may assert a claim of trespass because the premises are legally
his or hers.  However, in most states in which a tenant or someone living on the
premises is there against the wishes of the landlord, the police will not arrest that
person because the law requires an eviction action to remove a person living in a rental
unit. If the police could act on a landlord's allegation of trespass, most landlords
would be likely to bypass the usual mechanism for evicting people, which would deprive
them of due process.

Because of the confusion in the terms
you use, I cannot tell whether this is a situation in which someone has been abused or
threatened by a roommate or whether this is a situation in which someone simply wants
the roommate to be gone.  If the roommate is boyfriend or girlfriend, an order of
protection will result in that person's removal at least temporarily. However, if this
is simply a situation in which there is a desire for the roommate to leave, the police
will usually not act.  If the roommate is present with the knowledge and consent of the
landlord, it is up to the landlord to initiate proceedings to remove that person.  If
the landlord is unaware of the roommate's presence, the person who is the legal tenant
is likely to be in violation of the lease, so seeking help from the landlord could very
well result in the eviction of the tenant, too.

This sounds
like a complicated situation, so it might be best to consult an attorney.  Some cities
have free legal services for those who qualify, sometimes a county bar association will
offer discounted consultations, and universities with law schools often provide help
through legal clinics.  Your county bar association can help you find one of these
resources, if they are available in your area.