Short answer:
Maybe.
Long answer:
The purpose of an antenna tuner is to match the impedance of the antenna to the radio. Maximum power transfer occurs when the impedances are the same. As you've noted, this is very important for transmitting, as you want to maximize the actual radiated power. Plus, many modern transmitters will automatically reduce the output power when feeding into a large mismatch, to prevent damage. With receivers, it's a slightly different situation. There's no risk of damage with a mismatch. But it's still sometimes useful to match impedances, to get the most signal out of your antenna. I personally don't use an antenna tuner now, but many years ago, when I was more serious into long wave, I did use a homemade tuner, and noticed tremendous improvement. In that case I was listening with about a 200 ft longwire, which was extremely short (capacitive) on the longwave band. That was probably a worst case situation. About the same time, I was also using a tuner on shortwave, and while as I recall I did provide a small increase in the signal strength, it was not substantial. And it was a pain to continuously adjust the tuner when changing bands or even frequencies.
Another [positive] side effect of using a tuner is that it also often acts as a filter, rejecting stations from other bands. This can be extremely useful if your radio is overloading, say from a nearby AM station. Although in that case, a simple fixed high pass filter that blocks MW would suffice.
You can certainly try a tuner, and see if you notice much of an improvement. I would not count on a major improvement, however, in most cases.