Last time I tried GPE there were two big things not working for me- the GUI package manager was broke with no search function and GPE-minibrowser was nigh on useless as I couldn't access Yahoo! mail which is sometimes the only site I'll check. I would presume from that that it also cannot handle Hotmail and Gmail either yet.
I was speaking to Florian about this and he said no work had been done on the minibrowser recently. I'm sure most will agree that e-mail is in the top 2 uses of a computer for most people so I would say that getting this working should be a priority for the GPE team.
Just my 2p