It can stop you, but odds are it doesn't in many cases. IMO this is one of the biggest benefits of git over something like Subversion or CVS: its distributed, so you can continue to work locally while the origin is unreachable.

I can't tell you how many times in my svn past where I couldn't get any work done simply as a result of the repo sever going down or having some other issue affecting its reachability.

At least with git I may not be able to pull commits from origin, but I can still commit locally which is typically enough to keep me productive during outage periods.