Now that logmein has a free version...I'm wondering...if I set up my laptop as the local machine-hook it up to the internet at work, and log into one of my home pcs from my laptop....will that be a workaround for all the internet filtering on the work network?

It depends on what port your laptop is using for the proxy, what ports your work network are blocking, and whether or not it is doing something called deep packet inspection. Unfortunately, asking your network administrator about the later two will raise a red flag with him/her.
One way to find out is to just try it ... as long as there isn't a corporate policy in place remotely suggesting that you can't.