As of 2012, Google Drive apparently still did not support differential file sync. If that's still the case, Google would sync the entire 15 GB file every time it changes.
It sounds like you're using Outlook to back up your Google Apps Email, then you want to back up the Outlook PST file to Google Drive. You may want to take a step back and consider what you are trying to achieve.
- Do you want access to your old email in the event that Google has a massive outage? If so, then syncing the PST file to Google Drive doesn't necessarily help in that scenario.
- Are you trying to protect yourself in the event that your Google account is compromised? In that case, the PST file stored in the cloud would be worthless because someone may have tampered with it.
Using Google Drive to store your PST-file backup of Google Apps Email only seems reasonable to me if Google Drive is syncing the PST file to at least one other device that you own. But in that case, you could use some other backup system like CrashPlan, which lets you use your own machines as backup targets for free.
But let's suppose that either the email in your PST file is for a different email account than Google Apps Email, or you have a great reason for backing up Google Apps Email to Outlook PST, then uploading the PST file back to Google (Drive).
One solution to your file syncing problem is built into Outlook. If you turn on AutoArchive, your old emails will periodically be "aged out" into a separate PST file. This will allow you to shrink the main PST file enough that it can be synced in a reasonably small amount of time, while the larger archive PST file--which is only modified during an AutoArchive operation--will be synced much less frequently.
Another solution is to manually create a new PST file every once in a while and move all your old messages to that PST file (for example, at the beginning of each year). Assuming the PST files are purely for archival purposes, you could then unmount the new PST file so Outlook will make no future modifications, compact your main PST file, and let the main PST file accumulate mail for another year. This may not be quite as convenient as the first solution, but it will still be better than trying to sync a 15 GB file several times a day. As a nice side effect, it also decreases the chances that your entire email backup may be lost in the event that a single very large PST file is somehow massively corrupted.