That depend upon what type of connection you have! If you have dial-up modem then yes it does affect it. If DSL I 'think' it might affect it. But if cable, adsl, etc. then in most cases the answer is no.
If you are running as an Ultrapeer then you may get varying & unpredictable results. That's b/c people are going thru you help them connect to the network. It can use up a lot of your upld bandwidth. Being a UP could potentially slow your comp. UP can be disabled if prefered by going to Tools>Options>Speed & ticking Disable UP Capabilities & pressing the Apply button.
Also, do you use a usb modem? USB modems generally utilise the poser from your comp & also utilise your comp's processor. This may result in inconsistent results on both sides of the fence (your comp slowing & your connection not being consistent.)
Also don't use the Resume/Find Sources button on many files. Otherwise this will result in most of your files queueing for much, much longer than normal, & possibly affect LW's connection quality, & slow down both LW & your system by forcing them to use moe resources than normal.
Some hints: A well set-up LW can start to automatically continue its dwnlding after it's settled down perhaps 2 out of 3 times you open LW. Optimising LW & Maximising Uplds & Dwnlds A (1st post only) & also Part B which is even better & last & least are search & dwnld hints. The latter one I've been thinking about re-writing for some time. That's just for playing it safe. eg- I show all speeds & qualities.
Make sure your Java is up to date:
Java 1.5 (take the JRE)