Yes. The same as if you used polymorpist's jest to make it a 1/1 frog then take control. Once it's yours it's yours, even after the debuffs or spell effects are gone. The only difference is you need to leave Vedalkan Shackles tapped to keep control of target creature.
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This is the first deck that I've made public on purpose, so it means a lot to me to get a positive comment. Thank you.
look up the card Caged Sun and Cryptic Gateway.