Re masonry: apparently at least English ivy can.

We have a Hydrangea anomala subspec. petioilaris (climbing hydrangea), purchased about a foot high and planted against our fence 4 or 5 years ago. I subsequently read someone writing about climbing hydrangea saying it's an example of the old gardeners' adage re vines; "first it sleeps, then it creeps, then it leaps". Climbing hydrangea can reach over 40 foot with support. So I'm big on pruning our one.

Apparently, climbing hydrangea doesn't damage masonry, but it adheres to walls by "holdfasts" (modified tendrils). Removing a climbing hydrangea may involve cleaning these off the masonry, a labour-intensive (expensive) job.

At our ages, my spouse and I always have an eye to resale with a house. I'm familiar with what's currently in in kitchens and bathrooms, but I suspect that vines up the chimney stack are not (at least in our local property market).