Yes. Just make sure to download Squid from the same store (e.g. Google Play, Samsung GALAXY Apps, Amazon Appstore) and that you're signed into the same account you used to make the in-app purchases.
See Do I have to purchase the premium features for each of my devices? for more information.
Please note that your notes will be lost when you perform a factory reset, so make sure to back them up! You can create a local backup in the Squid Settings, or use the Cloud Backup premium feature to backup your notes to Dropbox and/or Box.