No, you cannot place these files on a network drive.
You cannot store them on OneDrive, Google Drive, Dropbox or similar service.

The database files (brd) need to remain on your local computer's hard drive.

These flat file databases are fast, light-weight, easy to use and backup - but their locking system is not designed to placed on a storage device managed by a system other than the local operating system. 

Placing these files on a local area network (server) drive or a remote (ie. cloud storage drive) will result in file corruption.

Backups and 'pushing' a copy to a co-worker
If your goal was to have a backup of these files - or to 'push' a copy of the data file to a co-worker:
--Please use our backup feature (File > Backup) and point to a remote/server drive. 
This will 'push' a copy of your file to the specified location.

DropBox, Box, Egnyte and One-Drive

Note: Do not use DropBox, Box, Egnyte, One-Drive or similar service as this will also cause file corruption.
Rather hear it from them?  
https://www.dropboxforum.com/t5/Dropbox-files-folders/Sharing-Access-database/td-p/148125

Did the above not address your issue - and you need true multi-user access?
You may need to upgrade to one of our multi-user platform, such as our Workgroup platform (or possibly Enterprise).

Subscription license upgrade to Workgroup ($40.00/month additional):
https://store.treasurysoftware.com/ProductDetails.asp?ProductCode=UPGSUB40PlatformUpgrade

Permanent license upgrade to Workgroup ($997.50 one-time additional, plus increase in annual support of approx $185 ):
http://store.treasurysoftware.com/product_p/upgprd1000.htm