Welcome from SW Florida, USA! Glad you found us but as James6591 pointed out you woud get better feedback over on the "Ruger Pistols" forum. This "Feedback" is aimed at using the website in general.
But to answer your question anyway, no, you cannot fire with the magazine disconnected due to the magazine disconnect mechanism. There is also an advisory in the owner's manual about dry firing with the magazine disconnected - don't do it.
I have an SR9c. I removed the mag dissconnect. I have never liked those on any gun. When I went to the range the gun worked great. I tried to fire a round with the mag out and it fired just fine. I will leave it out for now. One of the reasons is I dry fire it at times and its too easy to forget to put the mag in everytime.