In regards to IP addresses, no. Most internet service providers in the US assign/reassign IP addresses to their users constantly. Obtaining a dedicated IP address is seen as a premium service.*
However, most VPN prvoviders do have dedicated or semi-dedicated IP addresses assigned to their company. Although these also CAN constantly change and have new IP's added, usually, it is not often enought to be a problem. the task of blocking them is manageable, and there are even many public/paid list services which do this for you.
* Furthermore, there is a significant portion of players who play from Internet Cafe's, perhaps not as common in the US as in other spots, however, banning the IP will ban everyone there. I've seen this before actually, when some fool banned am internet cafe from a specific teamspeak server, now nobody at that cafe can access that server because 1 person did something
also there is this myth that a "gaming" vpn will reduce your lag. this is a simple illustration of the absurdity of this claim:
without VPN
A ----> B -----> C
with a VPN
A ----> B -----> VPN ---> C
(the only way possible that 'lag' could be reduced would be if an ISP is actively packet shaping gaming traffic. but then that would mean that the overhead of encryption would have to be less than the performace lag associated with extra hops)
Therefore it is my assertion that VPN users deserve special attention by Riot in general, if not an outright ban.