Don't know about the Boston Ivy being busy but you certainly would be. It would need regular (several times a year) shearing to keep it in bounds.

Why do you prefer plants in urns as opposed to planted in the ground?

If Yardvaark the champion of ivy, is counseling against it in this application, listen. I would ask what is on the other side becsuse they will have their own maintenance problem. Who owns the fence? Other than these cautions, I do think it would be an improvement. How about a less aggressive alternative?

Yard may be a champion of English ivy (as misguided as that may be :-)) .....but Boston ivy is a very different vine altogether! Oddly, here where English ivy grows with rampant abandon everywhere and on everything, Boston ivy is not very common and does not have any local reputation for being overly aggressive and I would not dissuade one from its usage. I planted it in my own garden to climb a fence and in 10 years, it still had provided only marginal coverage. But since we have no idea where the OP is located, I have no idea how appropriate - or not - it may be.

Fences make ideal supports for vines, especially vines that get pruned back routinely on an annual basis. I'd consider clematis, honeysuckle, climbing roses or even a climbing hydrangea for this purpose. Or any annual vine. None are so rampant that they will completely smother the fence or become maintenance nightmares but they all present enough of a flowering distraction that the fence/fence color becomes very secondary.

Where are you as far as nearest large city?

Do you have the option of staining the fence?

Have you considered the possibility of other vines that can grow on trellises rather than directly on the fence? If it isn’t your fence the neighbor might not appreciate the holdfasts that stick to the fence from the Boston ivy.

Why are so many plants in pots? That seems like a lot of work as opposed to in ground planting.

Have you thought about what you will do about the fence along the driveway?

The pots appeared after this post https://www.houzz.com/discussions/5703916/please-help-i-have-to-have-a-design-by-tomorrow-morning OP was in a desperate hurry to list the house in May, asked and receive a lot of suggestions but chose a different course. It seems the house was not sold after all.

OK, I didn’t recognize that it is the same yard.

I thought I would point out that Boston Ivy has a tendency to reseed itself around a lot. For example, my next door neighbor on the North used to have Boston ivy on the south side of her house before she resided it. Now I have lots of Boston ivy on the north and east sides of my (mostly brick) house! I don't mind this, as it adds a certain charm, but you do have to cut it back from time to time and keep it off the windows. In Fall, it usually turns a beautiful red color, but this can be inconsistent. It didn't happen last year for some reason.

Any climber that attaches itself to or otherwise blocks access to a wood fence will have to be removed in order to do any future work on said fence. Including re-painting or replacement of rotted sections.