If you aren't sure if the backrest will help or not, first go out and pick up a fat woman to ride on the back. If that helps, go trade her in at the closest dealer for a backrest. Don't forget to give her cab fare.
I tried riding without my backrest for the first time in a while last week. My back was already sore after about a 14 mile ride to the dealer. I took a 500 mile ride a few days later with the backrest on again, and I could have easily gone another 500, with no back pain. My advice is to get a backrest and don't leave home without it.
Also, the advice above about changing seats and handlebars also applies. I made the mistake on my 07 Road King. I changed the handlebars immediately upon purchase. After finding out how much the stock seat disagreed with me (backrest and all), I had to make a seat change, which necessitated another handlebar change.
It's difficult to determine if you are purchasing a seat and bars that will be comfortable for you by just looking at them. Get out to some bike nights and hopefully you will find some bikes that are the same as yours with different handlebars and seats. Don't hesitate to explain to the owner your situation and ask if you can sit on their bike to try out the feel. At least in my experience, I haven't run into anyone that minded a bit. When I owned a VStar, I saw a photo of someone's bike on a forum with a Mustang seat and he was fairly local to me. I actually contacted him to ask if we could meet so I could try out his seat. I ordered that seat as soon as I got back home from sitting on his bike. I ended up making a good riding friend out of that also.