I have a setup here, comparable to what 40H3X desribes. Two independent access points, non-enterprise. If you have SSID and password and some other traits exactly the same, the client can and will roam whenever necessary. That "necessary" is kind of debatable. Phones and tables try to be idle as much as possible, to save battery. But even these will scan the whole band every now and then. If they find a suitably equal SSID, they WILL step over.
There are few considerations though. Just the presence of another access point with the same SSID will not make the client switch, they will take other factors in consideration. Exactly which is implementation-dependent. In my experience, phones will delay roaming until necessary, that is e.g. when the signal strength becomes below -75 dB or even worse. Laptops will generally roam more aggressively.
The text which is quoted is correct, but only to a certain extent. Only on enterprise WLAN you have a feature called "seamless roaming" which means that when a client roams from one access to another, the client doesn't need to re-authenticate. This means there will be no suspension of service which you otherwise would experience for a few seconds, during re-authentication. On the other hand, many clients don't even support seamless roaming and also a few seconds interruption is not always a problem. So in my opinion the text is too black/white.
This ...
So a client device (laptop, tablet, smartphone), will choose first-heard during a channel-scan
... is definitly not true. Even my very basic esp8266 client considers signal strength when associating. I know because this feature was implemented recently
Also my phones and tables will re-associate when I move to another floor, eventually (because they typically will try to use the current one as long as possible). I have a setup with two access points on two bands (both 2.4 GHz and 5 GHz), the 2.4 Ghz access points share one channel, the 5 GHz access points use different ones. For roaming it doesn't matter much, although a "same" SSID on the same channel is typically preferred.
A common misconception about WLAN is that the access points determine which will be used to have a client associated. This is not true. The client determines the access point (and so also when to roam). There are some extensions to allow an access point to "suggest" to the client to roam, but the client's word is always final.
So to conclude, the above citation is not really true.
Edited by Erik Slagter, 18 November 2015 - 17:39.