I assume we're talking about romantic love and not just any kind of love?
But anyway: absolutely. I'm not really a Katniss and Peeta "shipper", but I do believe she eventually came to fall in love with him. Keyword: eventually. I don't think she was in love with him *or* Gale throughout the present-day events of the books. She couldn't be. Her world was made up of terrible things. Her love for her sister was the only love she was sure of. She couldn't handle the complication of a teenage romance.
I think she came to *need* Peeta before she fell in love with him. She found in him understanding and genuine good in a world that was harsh and cruel. He gave her hope and stability. It's clear from certain scenes in Catching Fire that a 'heat' had begun to form between them, but it's not until the end of Mockingjay when she's forced to really live without fighting a war or protecting her sister to keep her mind busy that she can open up to the inevitability of falling in love with Peeta.
Anyway, I've simplified a little, but that's my take! :-)
Oh, it's also worth mentioning that Katniss herself had a belief that love would lead to marriage which would lead to children, and so she opposed getting into a serious relationship throughout the books because she didn't want her potential children subjected to the Games. Once the Games are abolished, that fear is no longer valid and presumably she begins to let it go. Another factor in finally being able to openly fall in love.