Wow, old thread...but for reference:
Access tables (backend) will run just fine on a NAS. Just make sure your front end references the tables using UNC, and that your clients are accessing via 1GbE network. SSD drives must first be supported in your NAS trays (Qnap TS-470 Pro I know for sure as am using one) and will reduce latency on queries where multiple users are hitting the data at the same time, but a decent NAS over 1GbE is wire limited to about 110MB/s. I personally like using SSD drives in NAS because they have zero moving parts, and have proved very reliable in my experience. We're running a few virtual machines from an SSD in a TS-870 Pro to allow the larger RAID5 disk array (4TB disks) to spin down. The VMs hosted are 24/7 and would otherwise have the disk array spinning 24/7 too...a waste of power. Just make sure if you go NAS, that it is capable of decent performance. Tim has plenty of reviews here. I'm a fan of the TS-x70 Pro boxes as they are fast, allow very easy virtual machine hosting, and make offsite backup very easy via rsync.
If using a NAS as above, and Windows 8x, you'll also see performance improvements from SMB3, and asynchronous file access, so highly recommended if you can swing the client updates.
Up to a few months ago, we also used Access front end queries to pull data from remote (web server) MySql tables, so this is quite easy. You define an ODBC data source using a (free download) MySQL driver in C:\windows\SysWOW64\odbcad32.exe (for 64 bit windows) or c:\windows\system32\odbcad32.exe (32 bit) ...and use this data source on your front ends to link tables. I point this out because QNAP (and likely others) support MySQL and PHPmyAdmin out of the box. Don't be afraid of moving your tables there and using ODBC as above to link. Our Accpac ERP front ends work the same way to MsSql server. Database backups using MySQL dumps are also well documented, making disaster recovery pretty straightforward. If you decide you need remote access to the tables, your tables will be accessible if desired remotely by setting up ODBC as above, but pointing to your WAN IP and setting up a router port forward on 3306 to your NAS.
Also, in a small network, QNAP's QTS4.1 firmware supports domain controller functionality via SAMBA...so a free/easy way to centralize account/permissions management via the NAS without using a Windows server. I mention this as you are doing the peer to peer thing, ... Active Directory run by your NAS is there if required.
Hope that helps,
Cheers,
Dennis.