If a research building is connected to mosques via a blueprint and then the blueprint is deleted with no building being constructed, the research building will continue to be connected to the influence, with research updating as if regularly connected.
Blacksmith out of influence range.
Mill blueprint connects the blacksmith to influence area of mosques.
After cancelling the blueprint the blacksmith still benefits from decreased research time.
I tried to take out scholars from the mosques and the blacksmith updated the research time as if it were fully connected. Building the mill and then destroying it yielded the same result.