If you want to pursue B and have time to pursue B before A starts I would say go for it. You do not know if it is something you would like more than A until you do the interview.
I would not tell the recruiter about the offer unless there is a good reason to do so. You do not want the recruiter coming in and sabotaging your offer or pulling you from consideration with B which are both potentials. If you decide to take the job with B just let A know that you will not be accepting after all, there is no reason to tell them about B in any detail other than that you have accepted another offer.
If anyone is concerned about the ethics here just realize that if the situation at Company A changes and the OP is no longer needed they will not hesitate to retract their offer. The company could choose to have the OP sign a binding letter that would give company A recourse if the OP changed their mind. The problem with that is those go both ways, and the OP would then have recourse should Company A pull its offer. It generally costs much less to recruit someone else than it does to pay them should they no no longer be needed.