Yes. Just make sure to download Squid from the same store (e.g. Google Play, Samsung GALAXY Apps, Amazon Appstore, Windows Apps) and that you're signed into the same account you used to make the in-app purchases.
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.