Yes. They did see stars. Here is an excerpt from the Apollo 11 Transcript.
02 23 59 20 CDR:
Houston, it's been a real change for us. Now we are able to see stars again and recognize constellations for the first time on the trip. It's - the sky is full of stars. Just like the nightside of Earth. But all the way here, we have only been able to see stars occasionally and perhaps through the monocular, but not recognize any star patterns.
02 23 59 52 CC:
I guess it has turned into night up there really, hasn't it ?
This happened when the Sun was eclipsed by the Moon. So it was essentially night for them. There is no atmosphere, and there is no bright light from the Sun (there was Earth-shine though) which meant seeing stars would've been incredibly easy.
Here's a picture of the Solar Corona (AS11-42-6179). The Sun is eclipsed by the Moon. This photograph was taken a few minutes prior to the conversation above with Armstrong and Capcom.
They did not see stars on the lunar surface, however. Nor could a camera pick up the stars given the camera exposure settings. The human eye does not have the dynamic range to see the lunar surface (or any surface reflecting light) and stars at the same time. Astronaut Dave Scott did see few bright stars on the lunar surface but only when standing in the shadow of the LM for some time with his visor up. It is certainly possible to see stars on the Moon as there is no atmosphere, but that would only be possible if they look into space with no reflected light like the lunar surface or glare in their Field of Vision (that's how the Far Ultraviolet Camera/Spectrograph took photographs of stars on the lunar surface in daytime). It would also take some time for their eyes to adjust.
Seeing stars was easy though at night in Earth Orbit, Lunar Orbit, or when the Sun was eclipsed.
If you want to see pictures of stars taken from the lunar surface, here is a short video showing some of the photographs of stars taken by the Far UV camera on Apollo 16.