I think it's a wonderful idea to adopt a stray cat. As long as you two are getting along and it trusts you, then I don't think there would be a problem. The only concern I would have is if you have children. Depending on how long the cat has been roaming free, it might not trust people. Children might be upsetting to the cat (depending on their age).
My sister's first cat started hanging around their porch. She soon worked her way into their house. She was about 5 years old. It took some time for her to trust people. But, she fit into the family very nicely.
Let us know what you decide and how it works out. Post of photo if you bring the cat home. I'd love to see it!
