When my HTC Desire boots, I can first see a purple Android (?) icon, then a white background and the 'HTC' text, then a short animation with text 'T-Mobile'. Does that mean that I got a branded phone? The rest of the system doesn't show any signs of T-Mobile and I'm on a Vodafone prepaid 'contract'.
I'm worried that I got a branded phone (which means I'll get Froyo later than other HTC Desire owners) even though I'm not with T-Mobile.
Being that you get a T-Mobile graphic then I would say yes you have a branded Desire. Having said that my father has a branded O2 Desire and he has already received the Froyo update (today - Monday). I too have an O2 branded Desire, but I have not received Froyo yet which I suspect is because I am on a Business plan with O2, whereas my father has a personal plan.
I think all that matters is which phone you have and which carrier you are on. Updates are always pushed out by the carriers to their subscribers. So, Vodaphone will send out the update to all Desire's on their network, including yours, and you will be good to go.
If there is an issue when the time comes, then a quick call to your carrier should sort it out.