You can, but if the AP's aren't aware of their shared clients they can't hand them off to another AP when signal strength degrades. Let's say you connect a client to AP A, then walk out of range closer to AP B. Your signal strength will suck because you're now farther away from AP A (and close to AP B). AP A won't disconnect your client to allow it to connect to B for better signal strength (that is, until AP A's signal strength is too low to sustain a connection).
Networks that are meshed by design take this into account and communicate about signal strength per client, handing them over when they notice a neighbor would be able to serve the client better.
While communication between APs (and forwarding of the data to clients) helps, it's not strictly needed because clients will do background scans, especially when reception is getting worse.
It apparently depends on the client device's implementation but yes in general client devices will switch to connect to the stronger one automatically on their own
Networks that are meshed by design take this into account and communicate about signal strength per client, handing them over when they notice a neighbor would be able to serve the client better.