In my experience the connection speed and latency in game should be fine, the main problem is because of the size/security of uni internet. Most uni's use providers such as resnet will result in the NAT type always being strict, this means that you will be unable to connect to anyone who's NAT is not open and sometimes not even them, this mainly affects the time it takes to connect to online matches and will simply require a bit of patience (nothing to extreme just a few extra seconds), however if you are a competitive player in a console game such as COD, or like to host your own server on Minecraft (obviously you can not port forward your server, and only others on the same connection would be able to join) for example, this would require you to be able to connect to opposition who may not have open NAT, and there will also be many who struggle to connect to your host.
Basically if you are on PC you should be fine as you will be able to connect to most dedicated servers and the connection speed/ping should be fantastic, however on console you may struggle to connect/play with friends or set-up private matches/servers.