I would doubt if this would work but I won't recommend this.
In informed manner it is possible yes, I can not say for sure until which versions we would have the support, but it will be possible yes.
In Enterprise PDM for example, you may be up to 3 versions ago.
If you install EPDM 2015 you will have support for file SW2015, SW2014, SW2013.
Always recommended is the same version more I realize that sometimes it is necessary that difference.
No. Workgroup (pdmwg) and SolidWorks (sw) must be at the same major version. Service pack mismatches will work, but are not recommended - what if you get half a bug fix?
As always, make sure you have known-good (i.e.: tested) backup before messing around with pdmwg.