Yes, if you are serious about printing you should be calibrating your monitor. However, unless you are printing yourself, and calibrating monitor and prints, you won't get 100% accuracy. Most people can live with less than 100% accuracy.
I had a photobook printed a couple of years ago which came out dark, but was it my fault or theirs? Without a calibrated monitor who's to say? I wanted what I see on my screen to be the best it can in tone and colour so I got a calibration device, and also not have me having to compensate for printers that were printing brighter or darker.
Awhile later I got some free prints from Jessops (pre going bust) and when they were printed out I first noticed that the pics had been cropped (borderless prints) even though I had cropped them to 7x5. I asked if their machine was calibrated, and was told that their machine didn't need to be calibrated.

OK, maybe new machines didn't, what did I know. They weren't sure why the pics had been cropped again, so they said they would print them again during the week. The pics were the same.
They then said they would print a pic with the white border and the pic wasn't cropped. However, the picture was noticeably brighter and more colourful than the previous prints.

When I asked why they said their machine got calibrated every Sunday, but the girl who did it had been off for 3 weeks, and if I were to get any printing done in the future, get them done on a Monday.

Obviously not what they had said previously.

I was so preoccupied with the cropping problem that I hadn't noticed the other problems till I saw this newer print.
After that I went and got the same pic printed in every place I could in the city centre, both with and without a border. Sure enough all the borderless prints had been cropped again. But nearly all the prints were different for tone and colour. Some were very similar, as I think Tesco use Max Spielmann print machines in their stores, so those prints were very similar, but others were totally different. The variation was stunning.
Some print sites let you download their printer profile, which with a calibrated monitor may let you get very good prints other than printing yourself.
If you are not going to do that, I would advise getting a sample pic of your own printed in as many places as possible to see which gets closest to what you see on your screen.
Accurate printing can be a complicated subject depending on how accurate you want to be, how much work you want to do, and how much you want to spend.