Yes, you should be able to start them while stunned. Most will not clear the stun, however. It is more of "I need this bonus now and can wait for the stun to end" sort of deal.

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"I have no data yet. It is a capital mistake to theorize before one has data. Insensibly one begins to twist facts to suit theories instead of theories to suit facts."
- Sir Arthur Conan Doyle, Sherlock Holmes