OK, a couple of comments and a couple of answers.
If I split the database, will a FE file stored on a local machine successfully update the data in a BE file that is stored on drive?
Yes. In fact, once split, that BE file is the only place that SHOULD be updated. In a proper split, there is nothing in the FE to be updated.
What if two separate people edit the same field in their own FE files?
Depends on several factors, but generally the person who edits 2nd is the one whose update hangs around.
Now, as to the shared Google drive, you will not have really good results if your network develops any hiccups at all. But my question is about your network structure. From the way you talk, everyone is on the same network at your office. Is that true? Because if you have everyone on the same in-house network, you can add just one more machine on the network that you can leave running during business hours, one that is set aside for this purpose. You can place the BE on that machine. It does not have to be a server. I.e. not running Server 2012 or some other specific version of Windows destined to be a server. The protocols used by Access DO run peer-to-peer. At worst, you might have some tricks to play to get the file permissions right for the folder holding the BE file.
If you actually have remote users, that can be a serious problem because they can't so easily be on the same network in that case. In that case, you would need to look to RDP or a product like CITRIX to manage that safely.
The reason we are pushing you away from the shared Google drive is that not all of those cloud-like drives permit the protocols that you need for Access. And one last thing - an explanation of something you said in your first post.
With excel, word, or powerpoint, the real-time presence notifies us if another user is editing a file. Unfortunately, access has no notification that someone else is using the database,
This is by design because of the difference in protocols used by the various utility programs. None of Word, Excel, or PowerPoint are designed to be real-time shared, but Access EXPLICITLY is designed to do this. That's why I mentioned protocols earlier. When you open a Word, Excel, or PowerPoint document, edit, and close it, you replaced the ENTIRE file in the process. That is, the file is not selectively updated. It is totally replaced. But with Access, you CAN and often DO replace just a part of the file. AND when you do, the other parts of the file remain as they were, very likely occupying the same disk blocks as they did before you opened, updated, and closed the file. Access uses a protocol to allow that fractional update through the file system whereas Word, Excel, and PowerPoint do not. Therefore, since you are going to totally replace any of those files, you don't need that fractional protocol (called Server Message Block or SMB, a member of the TCP family of protocols).