This is hard to answer.
It's fair to say most Android users will have a Google account and won't be bothered by having to register via Google.
But how many people ARE bothered by it? How many people won't use your app, because of this?
This I can't answer and you can only find out by launching your app and viewing number of downloads vs. number of registrations. (If you do a little bit of digging I bet you would be able to find stats on the average number of users who download but never use the app. Adobe says it's 25%, but it's not mentioned in the source they mention)
I've once read a related article from a company saying why they removed the social media logins from their app. According to them they were never used. This is interesting, but they offered multiple options next to a normal login with email/username and password. I'm one of those people that prefers the normal login over social login, because I want to give as little personal information as possible whereas with a Facebook login they sometimes want to know what you like and post for you. In most cases the app will never use the personal information other than as authentication, but the user does not know this. But when not given the option, I'll use social logins. Perhaps more people are like me.
PS I know on iOS it's possible to instantly start using an app, because iCloud is used as authentication in the background. This removes the hurdle of registration. But I don't know if this is at all possible for Android.