Quick and dirty answer, no, every device affects the speed of all others.
Now for the real answer. Those 3 Mbps (or whatever your ISP sells you) are the total speed of the connection from the modem to the outside world. That link is the one capped at that speed, by your ISP according to your plan. The LAN part is entirely on your side and whatever you do that is irrelevant of the internet connection, hooking a computer by wired or wireless does NOT affect the internet speed (again, set only by your ISP).
But when those computers are connected to internet, though the modem, all those use a different LAN port to reach it, but after the modem all of them share the same internet line, hence the bandwidth is shared, usually according to the usage each computer is doing at the moment. Wired connection will buy you nothing in terms of internet speed, but will greatly increase LAN transfers (between your own computers) over a wifi connection.