Are you using a smartphone or a computer for the queue?
Because it makes quite a difference. Ticketmaster's virtual queue works like this: the system assigns you a position in the list when you access the sales page, and technically you can close everything without losing your spot. But there's a detail that others haven't really stressed: it depends on what you mean by "closing the window." If you only close the browser tab and keep the browser open, you're usually fine. If you completely close the browser or even worse if you clear your history/cookies, then yeah, you're risking losing your session.
Wait times vary a lot, from a few minutes up to an hour or more depending on how many others are after the same tickets. In the case of Måneskin in Rome, considering the almost guaranteed sellout, it could be pretty long. The most important thing is: once your turn comes up, the system gives you a time limit (usually a few minutes) to complete the purchase before your ticket goes back on sale. So yeah, you can step away from the computer while you're waiting, but when you hear the signal (or when you see the page refresh telling you it's your turn), then you need to act fast.