Connect the hose, it's doing exactly what it's supposed to. Think about it, at idle manifold vacuum is high and because you don't need a lot of fuel the regulator drops pressure. When you plant your foot on the gas pedal (really the air pedal) the throttle plate goes wide open and manifold vacuum goes very low so the regulator boosts pressure.

The computer has learned to deal with the problem but it will eventually learn to run even better if the hose is connected. It will take some time but if you want to speed it up you can remove a battery terminal, turn the ignition switch to the "on" position for 10 minutes and then turn it off and reconnect the battery.

It means the FPR is likely bad with a leaking diapraghm or your fuel pump is on its last days.  Yes, leave it alone.  It is not broken, do not fix it.  When you get a CEL with a code that says the engine is running lean (P0171, P0174) or a P0300 (random misfire) or the car does not start, then it is time for a fix.  Do not forget to bring your cell phone every time.  Good luck.

It takes a while for the ECM to learn how to handle a change in fuel pressure and many other things. While resetting the ecm will maybe speed up the process, it also poses other problems. Like maybe having to enter security codes on radios and maybe anti-theft devices.

If you reattach the hose, it will improve the fuel efficacy in theory. At idle the fuel pressure is often dropped so that the engine is not running rich. Running rich can foul plugs and also cause a failure of the converter. While plugs are not expensive the converter is.

So I suggest putting up with the sluggish issue for a while and just reattach the hose.

If you reinstall the hose, you should disconnect the battery cables and touch them together for a few minutes. That will wipe out all the computer memory so it can start relearning with the proper fuel pressure