I just got through uploading a v7.01 to Brinkster (free account and what a pain in the arse) for a friend. Yes you can use it.
You will need to upgrade the database using the Mirgration Tool first.
**Make sure and Compact and Repair the 6.34 database prior to upgrading and do the same once the database is upgraded.
**Also, once upgraded you will need to login with the default user/pass for a new forum. Then go into the Admin and use the Change Admin Username function to change it to your old user/pass from your v6.34 board. Resynch the topics and your old posts should relate back to your name.
Then you will need to upload all the v7.01 files to your Brinkster account and setup your forum just as if it were a brand new one.