Googlehater I don't have sandboxed play services installed on my grapheneos device.
Will this app work?
Maybe.
It is advertised as an offline inventory management app.
As i want to manage inventory this is the last app i have found to try but the google code inside the app concerned me.
If the app work, will it talk with google?
I can't see any reason to have google libraries installed if it isn't going to communicate with google, so I would assume yes.
Should i download the app if i am a open source only degoogle everything kind of person?
Probably not, however this assessment is based on a philosophical position rather than a practical position.
Or can i use the app if it works because i can denie network permission anyway even the app is advertised as an offline app?
If its truly an offline application, then that's a good option.
BUT NOTE: With google services being part of the application, there is a potential for data to be communicated to and from other applications with google services.
The app seems to be open source but i can't find much about it online.
If it is open source, you should be able to find the source code repository and inspect the code. The code itself will be much more competent at explaining what it is doing than anyone here making guesses about it based on theoretical worst case scenario.
In fact if it is open source, you might even consider modifying it to disinclude the google libraries altogether.
If it claims to be open source, but there is no source, then it is not actually open source. If that's the case, I would be very skeptical of the software since somebody is lying about it.