The mother seemingly exposed to alchemy a lot must have tried it herself sometime. If anyone could be an alchemist that is. She might have been a state alchemist once who knows? If she was an alchemist she could have been a little help to Edward and Alphonse.
Taking a look at the wikia page, the brothers "would always try to cheer her up with their alchemy. In fact, Alphonse once said that their mother's happiness was part of the reason that they continued their research in alchemy because it made her smile. However, they didn't realize that she smiled because it reminded her of Hohenheim and his own talents in alchemy."
So as lentinant said, no.
There is no canon evidence that points directly towards it however it is never stated that she didn't know anything about alchemy either; so if you'r headcanon is that Trisha was an alchemist it's not 100% unrealistic, just slightly unlikely.