Yes. In aperture priority, you choose the aperture and the camera chooses the shutter speed, so it may pick a speed that is too slow for moving people. If avoiding motion blur is your priority, use a mode that lets you control shutter speed instead.

Best options:

• Shutter priority (Tv): set the minimum shutter speed you want, and the camera will choose aperture (and ISO if Auto ISO is enabled).
• Manual + Auto ISO: useful if you want to control both shutter speed and aperture while letting the camera adjust ISO.
• Program (P): on some EOS M bodies, this gives you access to ISO control while the camera chooses shutter and aperture.
• Sports scene mode: may bias the camera toward faster shutter speeds.

The trade-off is simple: raising ISO helps you get a faster shutter speed, but it can increase noise. In many situations, a slightly noisier image is preferable to a blurry one.

So if shutter speed matters, aperture priority is usually not the best mode.