If I buy an unlocked sim-free HTC Desire HD can I still get Android updates OTA? I currently have a HTC Desire with T-Mobile.
If I buy an unlocked HTC Desire HD (Sim-free) and pop in my current T-Mobile SIM will I get OTA updates for the Desire HD or the standard Desire that I have with T-Mobile?

If I won't be able to get OTA updates, will I have a manual update option from HTC direct when they release updates?

I've never bought a Sim-Free phone before so not sure how this works.
AFAIK, Android updates are released by the Google then the phone's manufacturer (e.g. HTC) writes updates for the drivers, and providers (e.g. T-Mobile) only help with the distributions. So you will at least be able to do manual updates as long as your phone manufacturers released the update.

However, this means getting update depends on your phone manufacturers support (I heard HTC is quite good on this). If, for example, your manufacturer decided not to support updating of your phone (e.g. Samsung has no plans for updating Spica to Froyo), then you probably won't be able to update using official ROM (although there is almost always a community update to non-official ROMs).