No.
The issue type is not a simple field, it's a structural thing. A lot of configuration hangs off it - fields, workflows, and all the associated stuff behind that. Changing types during a workflow transition would break spectacularly - it would be like changing the chassis of your car. While you're driving it at 70mph along a motorway.
It's actually quite hard to do it later as well. You can "edit" the issue type, but only if the old and new types are using the same configuration (the car is stationary, and you're swapping one chassis for an identical model). Otherwise, you have to use "move", which has all the checks you need to ensure the configuration won't break. In theory, you could do that edit with a listener, if the config was close enough, but you'd need to replicate all the checks and updates "move" does, or rely on your admins not changing the config enough to break it!
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