What is the reason that they host these databases on their local machines? What database system do they use (MySQL, MS-SQL, Access)? My first inclination is to move all of the databases to a DB cluster. It doesn't solve your space issue, it just moves it from virtual desktops to virtual servers (where the space can be better consolidated and more effectively used).
But barring that, storage space is NOT expensive. In fact, it's so abominably cheap, now, that you can get petabytes of SAN space for less than the cost of the Windows licenses you'll need to set up your VDI environment (depending on the number of users).
And that's where you need to go, is a SAN. You can provision 2TB LUNs and host those as shared drives on a dedicated Windows server, or NFS shares via Linux, if you prefer. Your only concern, here, would be performance, and if your network infrastructure can't handle hosting your data over a SAN, then it can't handle VDI anyway.
Update: Ooooh so they're looking at a 3rd party VDI solution. That's called IaaS - Infrastructure as a Service. It means putting all of your sensitive data onto someone else's server in someone else's data center where you have no control - and I'm not sure how that's any more secure than using a local workstation. But that does explain why space is expensive! You could probably buy petabytes of storage for the cost you'd pay a host to lease a few terabytes. There are pros and cons to IaaS, and in my opinion security is still a con, along with cost.
But, if all of your VMs and DBs are on a shared drive, that should be fine as long as the host has a decent infrastructure (and they'd better). A shared drive is actually better, since it consolidates your storage and wastes less space. You actually ought to be able to get away with 30GB per desktop with your "My Documents" etc. all hosted on a single shared drive and your DBs etc on a separate shared drive. You might find that you can fit your entire organization's data on 4TB.
The biggest advantage of VDI (if the host's set up right) when working from shared storage is that your desktop is running on the same 10GBps network with your storage SAN. That network is technically faster than the innards of the latest gaming desktops (HDD SATA speeds only up to 6GBps). The SAN has massive storage arrays with multi-raid configuration that can fill that 10GBps without a hiccup. Your desktop is also running on a server farm consisting of several very powerful servers, each with upwards of 128 cores and more RAM than you could shake a stick at. Soooo you ought to see improved performance in the VDI. If the host is set up right ;)
1If you want to satisfy my curiosity, what is your role at the company? The way you phrase your question suggests that you're not quite a developer and not quite IT. And it also makes me wonder why your company is moving to VDI in the first place. – Thomas – 2014-04-03T17:35:38.383
I am a developer; I wrote the question quickly and could have worded it better (will edit now). We're moving to a VDI because they say it is more secure and controlled. Our company handles sensitive data which we're legally required to protect, watch and audit; luckily that's not my job. – AlexMA – 2014-04-03T22:47:25.027
I've updated my answer based on your updated question :) – Thomas – 2014-04-03T23:42:26.390