+1 for a dark site with an 80mm scope.
A UHC filter rejects a lot of light. I've never tried on in an 80mm scope, but my guess is your view will be very dim. I got tired of being disappointed by the view of deep sky objects when viewing from my driveway, so when I'm home I only observe the moon, planets and double stars. I save the other deep sky objects for trips to my club's dark sky site.
I use UHC, O-III and H-beta filters in 80mm scopes all the time. I even use them in my 50mm finder.
Filters do reject a lot of light, that is exactly why you use a filter, it rejects the light you do not want, it passes the light you do want. The Lagoon nebula is very rich in O-III. Using a filter rejects the vast majority of the sky glow, dramatically increasing the contrast on the nebula itself. Stars will also be reduced in brightness, the purpose of a nebula filter is to improve the views of nebulae and for that they are very effective, even is small scopes if used properly.
If you figure that a good O-III filter has a band pass of about 14nm and the visual spectrum is about 200nm, the contrast of an object like the Veil or the Lagoon will be improved by as much as 3 magnitudes. A good UHC filter could reduce the skyglow by about 2 magnitudes.. This translates into views that are similar to a dark site.
My backyard in San Diego is red-zone, on a good night, it is about 18.6 mpsas directly overhead, that's translates to something like magnitude 4.5 NELM. Three magnitudes reduces the sky glow to 21.6, two magnitudes, to about 20.6. As one might expect, this means that nebulae are much more easily seen.
I have seen both the Veil and the Helix nebulae from my backyard in an 80mm scope. One of the keys is not using too much magnification. The brightness of the sky glow and the nebula itself depends on the exit pupil one employs, at a 5 mm exit pupil in an 80mm (that would be 16x), the image of the nebula is just as bright as it would be in a 400mm telescope with that same 5mm exit pupil.. The difference is that in the 400mm scope, the object will be magnified 80 times rather than 16 times.
Nebula filters do work from urban skies in 80mm telescopes.
As far as observing deep sky objects from an urban sky.. I enjoy it. It's not like observing them from dark skies, which I am fortunate to do a week to two weeks per month. But I take what I can get, with a cup half full, there can be plenty to see and observing under light polluted skies is good practice.
How much it would a UHC filter dim the image in a scope this size? I believe most UHC filters are designed with bigger telescopes in mind. It sounds like people are recommending the UHC over a light pollution filter, which is good to know
.As you can see, UHC filters, O-III filters, they are designed for scopes of all apertures. They only work on certain specific objects but for those objects, they are spectacular.
Don Pensack (Starman1) has a comprehensive Filters Buyers Guide at the top of this forum, it's a good read.
Looking at the Olivion 1.25 inch UHC filter, it looks to be quite reasonable, especially considering the $53 price. It has a bandwidth of 30nm, very similar to the Orion Ultrablock which has a 29nm bandwidth.