No, he was going to be killed at helgen.

I think that the plan was to hurry up and off them all there, but the Thalmor no doubt probably wanted the solitude thing to 'happen' so they could stage some kind of escape for Ulfric later.

Here's a tip:

Thread title: Ulfric's execution
Opening post: your question

You're welcome.

Ahem. They were going to execute him in Helgen, along with rest of the (alleged) Stormcloaks.

Tullius didn't want to a public spectacle, such is the nature of the beast. Plus, 'then and there' makes it a lot harder for the Thalmor to do anything about it.

As an aside I had hoped to find a journal or some such from Elenwen that elaborated on how they had planned to get Ulfric free, had Alduin not appeared.