I understand where you're coming from a bit better now. I'm not a techy by the way, just a primary school teacher who has been trYing to sort this out all week whilst still teaching full time. I'd had no prior exp of using a mac, or MDM servers until last week, either. I completely share your frustration.
You CAN enrol them on the programme with their existing apple id.
Using your MDM (I use profile manager so this will only make sense if you're using the same) you can add a user to OS X server. This user will now show up in profile manager.
Once this user has been added (just a username and password will do) tell the user to use their iOS device to visit your server name in Safari e.g. mymdmserver.local/mydevices
This will allow them to 'enrol' the device. Then get them to click on profiles and download the trust certificate and any other settings that appear there (ones you have created)
Once the device is enrolled, if you go to the groups section in profile manager, you can select everyone. Select the about tab then go down to VPP Enrolment then select 'send invitation to devices' - this way you don't have to send emails. now, provided your user has enrolled, they should get a box pop up on iOS device saying they've been invited for your organisation to send apps etc. this will ask them to sign into their own iTunes account. This now enrols that account with the VPP programme.
get the user to check they have automatic downloads turned on in their settings. Once all this has been done you should be able to push the apps from profile manager as long as you have added your VPP token to the OS X server profile manager section (not the web bit)
Add all the apps to a user or group in profile manager (web portal) then push. (Then you might experience the problems me and other forum users are experiencing regarding free vs paid, but a couple of tickets have been opened now and Apple are investigating) but your devices will at least be linked to your VPP account.
Now, what we had to do was add all permutations of the Apple iTunes Store to an allowed 'site' otherwise it WOULD NOT work. You could always ask them to just add specific device mac addresses eg, that of the Mac and those of the iPads to access the iTunes Store (and it's many many different addresses!) Might be one you have to fight out with your IT techs as the server and the devices will only be able to download when your server is running, which I presume will be in your building unless linked to your active directory and network.
And if this doesn't help, then I give up :-S