I have tried growing morning glory through roses, and climbing up tall lilies. But it was too vigourous, and I had to remove it in both cases. It can act a bit like bindweed (though not perennial). It might possibly work with bigger and stronger shrubs. No harm in trying it out of a basket.
As a matter of interest, ipomea is regarded as a pernicious weed, every bit as bad as bindweed, in its native habitat (Florida, I believe), where it is a perennial. Luckily, we don't have that problem here - although you may find that it seeds heavily, and you get a lot of babies next year.