Yes you will almost certainly see a dramatic increase in messages and aircraft. The airspy is far more capable than the rtl dongles.
I’ve never see more than 1800 msgs/s with 1600/s being more typical. The airspy regularly gets around 3000/s. I’ve seen over 400 aircraft simultaneously with the airspy.
I think waiting to see what performance you get before cutting the coax is probably a good plan. You might find it’s not too much of a problem, though getting the amp as close to the antenna as possible is ideal.
Sell it and get the rtl-sdr.com triple filtered one instead. The filtering on the current version is not as tight as the original, but it should still be good enough. I’ve been using one for a couple of years and it’s performed very well. It also has higher gain than the uptronics amp.
I suppose you could put a narrow band filter on the input of the amp, but it would probably cost you as much as the triple filtered LNA and wouldn’t be guaranteed to help.
You might find this thread interesting for seeing where your signal is getting blocked if you haven’t seen it already: Signal Strength Heatmap