As far as I know the answer is no.
The only way I could see this working is if instead of a "quick filter" you used a filter sheet.(just a sheet that has a vertical list of the items you want to filter as) you can format it to look a lot like a quick filter but it's fairly obvious it's not checkboxes or radio buttons.
You can then assign two click actions to the filter sheet (1 for the filter action and one for the URL action)
It's not as versatile as a quick filter but it will change your photo URL at the same time.