Maybe is a better answer. You'd need to install a program to read HFS+ formatted drives, which does not come standard with most Linux distros.
The other (more technical) issue is that Time Machine uses hard links to do its magic, which is why you are having your trouble in Windows. Linux understands hard links of files, but Apple broke a long-standing Unix rule when they made Time Machine and allowed hard linking of directories (note: this is not a bad thing--it's the only way Time Machine could work the way it does). What this means is that you will likely have just as much trouble reading the disk in Linux as you did in Windows, because Linux doesn't understand hard linked directories.
Basically, you are out of luck unless someone develops a Time Machine reader for Windows or Linux. The only other thing you could try is doing a search for the file (not the directory) that you want, but this will likely take a very long time, and might crash the search, depending on how it deals with the links.
Better option would be to find a Mac and read the file there. And then stop using Time Machine for backups, unless you have no plans to try to access your backup on a non-mac.