Yes it absolutely does, but it is dependent on the station (the client) doing so. One of my gripes about Wi-Fi is that it delegates too much to the station - your experience is thus dictated by whoever wrote your phone/computer's Wi-Fi chipset driver, and how they interpret the standard.
Any Wi-Fi network supports roaming on the network side, you just need all of your access points to use the same SSID, and to dump users onto the same subnet consistently (otherwise you'll need to re-IP after roaming).
Any Wi-Fi network supports roaming on the network side, you just need all of your access points to use the same SSID, and to dump users onto the same subnet consistently (otherwise you'll need to re-IP after roaming).