Apache would run, and while you're in the remote session "localhost" would behave as you expect. But, in general VDI environments should only be applied to highly controlled and similar desktops (a developer would very rarely be happy or productive in a VDI environment; with some specific exceptions).
There are three "pillars" of VDI (as according to me)
- Standardized; the employees on the system all run the same set of applications (more or less)
- Managed; tightly controlled environment (without extremely tight security controls simple mistakes turn into widespread outages as employees could directly impact each other).
- Scale; the CapEx on VDI projects is substantial and rarely makes sense for less than ~50 employees (this does vary quite a bit depending on situation). The OpEx makes up for this initial expenditure fairly quickly if #1 and #2 are implemented correctly.
I don't pretend to know exactly what software or control over your "local" machine you'd need. But most developers want Admin privileges, which conflicts with #2. Also whatever development applications you use are likely to not be used by anyone else, even if you're just using something simple like Notepad++.