Yeah, it will harden way too fast to do that. Like the other commenter said, use glue to stick them together, then you can weld the seams, and also add some extra filament if you want a smoother seam. I just welded that print as it's all held in pretty tight in the drawer. There's almost no gap around the outside at all. I just welded and there is a visible seam, but it's minor and I don't need it to be perfectly smooth. If you wanted it to be perfectly smooth, I'd add filament and then sand it flat and possibly paint if you felt inclined.

As far as strength, like I said for this print it didn't need to be, but it really depends on what you're making. Use your best judgement, CA glue bonds very well. I use clear gorilla glue myself. It doesn't expand like normal gorilla glue. But yeah, I use a combination usually depending on what it is. Like I said, just use your best judgement and definitely keep the parts together and weld along the seam instead of melting and trying to stick together, lol.