Does purchasing honey help or harm the bee population?

It is a net gain. Substantial funding is provided for research specifically on Honey Bees to ensure their proliferation and success. If Colony Collapse Disorder happened to another non-honey producing species, no one would care and bees would probably be an endangered species. Instead, it is of an international interest that we protect bees as they are part of a very important symbiotic relationship with honey consuming humans. See to for what happens to other bees.

Bees are not killed in any significant way by harvesting honey from commercially provided hives.  Rather, providing an income for beekeepers allows them to provide more hives and thus reproduce more bees, collectively.  Only when wild hives are harvested are bee colonies actually destroyed by collecting honey, and such practices are limited to traditional, rural societies and occur in very small numbers, so you're not going to be buying that honey in any case.

I raised bees as a child. Our best year we harvested 1,980 pounds from 30 hives. That includes a spring and fall harvest (very different flowers and very different taste). Harvesting honey doesn't hurt the bees at all. The only harm comes from bees which sting you, which is rare. This kills honeybees. In a year I got stung maybe four or five times, working with them for many hours a week. With the money we made from honey we were able to capture wild honey bee swarms in Spring and domesticate them, and divide hives with new queens, increasing the population. This was in the seventies before Africanized bees were in the wild - I probably wouldn't do this today. So, I'd say buying honey strongly increases the population. Buy from a local apiary if you have one - or mail order it. Lots of small hobbyists out there with the much healthier and delicious non-pasteurized honey. Honey is stable and antibacterial, so pasteurization is silly. Some very young (less than a year old) children have died of botulism from raw honey, but it's very, very rare - botulism can't reproduce in honey but it can be included in very small amounts and lie dormant. Adults are immune to it in small amounts, just don't feed it to infants.

There's a significant net gain. Buying honey encourages its production, meaning the both the need for more bees and a chain of employment and profit in the supply chain. The need for more bees means that bee keepers have more hives, which in turn are often moved around in order to maximise the honey taste and production. This movement of hives helps local farmers with the pollination of their crops, resulting in higher yields. Bees employed for honey production often stand a better chance of surviving bad weather and/or overwintering because of better quality hives. Out of season, those same bees are fed a sugar solution which often contains small amounts of added vitamins and minerals to keep the bees healthier.

Let's narrow it down to one colony of honeybees on my farm and look at this. I might pull 10 frames of capped honey off of this hive.  That's approximately 30 pounds of honey, give or take. Now if I can sell those 30 pounds of honey (typically this is not a problem) then I can net perhaps $210 for that honey. With that $210 I might spend some percentage of that money on more beekeeping equipment and split the colony into two. That will, after some period of time, effectively double the number of honeybees on my farm. Now, the bees will fly 3 miles if they need to - actually, they can fly maybe 5 miles if they really need to fly that farm - in order to find pollen and nectar.  They'll seek out flowers and some garden veggies and flowering trees. Many of my neighbors' gardens benefit from those bees. And buying my honey encourages me (to some extent) to keep bees. So it certainly helps the population.

Stop purchasing honey will hurt bee population. If demand decreases, it would not be economical to maintain a bee population for honey production.