There isn't a problem exactly, it's just good to understand what doing so means.
The three Google Play Services apps are sandboxed like any other apps on GrapheneOS. They'll require network permissions and Google Play Services will need unrestricted battery usage for push notifications, e.g. for Protonmail. They don't need any other permissions.
To understand what installing these apps mean, you could read this to see what each app in a profile can see. That way you know what information Google will be able to see.
https://hub.libranet.de/wiki/and-priv-sec/wiki/what-can-apps-see
You could always use Aurora Store or Github to update those apps. As long as you have a way to keep your apps up-to-date. Then you wouldn't need to sign into Google Play Store.