We have 3 Google WiFi points. My son has one in his room that I access in my office and my other son accesses in the other room. The one in my son's room has an ethernet cable connected to it... does this slow down the speeds for me in my office and my other son's room???
Having an ethernet cable in one of the points wont slow down the network, but depending on how much bandwidth each device is using can slow it down.. but that would be regardless of him using an wired or wireless version.
bottom line, if has a hardwired device, that means less wireless activity, so this should be a net gain for other wireless users.
Do you mean the Wifi point is hardwired to another Wifi point or it has a normal device connected to it? If you mean you've hardwired it to another Wifi point, as Ashepherdson rightly mentioned, hardwiring a Wifi point should generally help. However, you should be aware that a Wifi point prefers the fewest possible hops back to your primary Wifi point, over anything else. If a Wifi point can get even a weak connection directly to the primary point, it will use that path instead of going through another Wifi point placed in between (this potentially results in poor performance for devices that connect to that Wifi point). They will form a multi hop topology, but only if they can't get a single hop path to work. That's why the best thing you can do is place your primary point as close to the center of your home as possible, with your Wifi points around it to expand the total coverage area.