Yes: The NI-VISA driver should always be backward compatible with older applications. If not, that's a bug. While newer VISA versions expose functionality that newer LabVIEW versions take advantage of, we don't remove functionality. It may not be as optimal, but it should work.
But not officially tested: I don't think we explicitly run our NI-VISA tests against LV 5.0x any longer. NI-VISA 2.6 did explicitly support that version, whereas NI-VISA 3.0 explicitly supports LV 5.1 and higher. I don't think anything significant changed between LV 5.0 and 5.1, so you should still be OK.
If you install NI-VISA 3.0x onto 2 different machines, 1 with LV 5.0x and 1 with LV 5.1, the only difference should be that the LV 5.1 machine will have
additional functionality of the newer VISA version. In other words, we will update the new properties and methods that VISA has added since that LV release. But if you have an existing application and don't need the newer VISA functionality (in other words, you just need the bug fixes), then this shouldn't matter.
My suggestion is this: base your decision on the readme file. If it mentions fixes to issues that are relevant to your application, then you should feel safe doing the upgrade.
I hope this helps.
Dan Mondrik
National Instruments