TB and TBP sync? And: slow startup in public library

i have a computer at home, and sometimes it's connected to the internet and sometimes not.

for those times without, i tried TBP as found on portableapps, and went to use it in the public library. the start-up is really slow and sometimes the computer hangs... there's not much i can do, i don't have administrative rights on these machines and time is short.
(the computers are fast enough otherwise, i think the anti-virus is on some kind of paranoia mode or removable drives get triple checked or sth.)
however, i tried other mail programs and they are quicker, but none of them really satisfying.

see, i'm looking for a long-term solution.
the best solution would be to be able to run two TB, one on my home computer and one on my usb-drive, sharing the same files. i guess this is called sync.ing.

so, two questions:

1) is it possible to sync TB and TBP?

2) is it possible to set up TBP so that it starts up faster, communicates less with the local computer or the internet (i mean during startup!!!), or?

thanks in advance.
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PS: i would be willing to change to a different product altogether, if it works nicely from usb at home as well as elsewhere but i want to give it some consideration...
and i wonder if other people have this vision of a portable application that can be docked to it's mother application at home...