Can I use Google account to store contacts and events without synchronizing them in Google cloud
Yes you can store contacts and events in your Google account on your Android device and don't synchronize them in
Simply disable Google synchronization on your Android device:
Menu Settings/Accounts & Sync and uncheck Google synchronization. Then your data will no longer be synchronized with Google cloud.
But you will still be able to synchronize this data with BirdieSync if you selected your Google account to be synchronized for contacts or/and events in BirdieSync options, Contact or Event tab on your Android device.