I hope so. I did wonder when you said you had an old laptop whether you were stuck with USB 1.1.
USB 1.1 through put is about the same as 802.11 b (12 Mbps). If this forces your adapter into that mode, it will slow your WLAN down for anyone else using it. With a USB 2.0 hub you should get 802.11 g (54 Mbps) so yes it will be faster. Fast enough to watch streamed video (if your laptop can keep up).
I would hope it is more stable. Although your adapter claims to be USB 1.1 compatible, that won't have been tested as much. I've had wireless disconnects while transferring large files to another machine. I guess something couldn't take the load. Overload might be why you loose the connection while you're busy. That should get better with a USB 2 hub. You don't want the wireless going down and taking your VPN connection with it.
Interference is another possibility. Does the Network Manager report other wireless networks in your neighbourhood ? Are they on the same channel ? If so, try using a different one. It is said that things like cordless mice and cheap electrical equipment can cause interference too.
Anyway, best of luck. Let us know how you get on.
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