Yes. In fact, many local meets do not have any masters categories so you are competing against the Seniors anyway. If you are in one of the few local meets that does have a masters category, just tell the meet director and he should be able to handle it however you want. There have been local meets where I have medaled as a Senior and as a master.
At USAW national level meets (American Open, Nationals), they do not have a masters category so if entered you are automatically competing against the Seniors.
And consider going to a Masters only national meet – http://www.mastersweightlifting.org/