Yes, you can always enter info manually. If this is for the 1099-K info, you will just go to the 1099-K section and manually enter it. If you track all of your business income together, then you do not need to separately enter the Square info as this will cause the income that is double reported to be taxed twice.
If you ONLY use Square, then entering the information manually or allowing it to be downloaded will not change anything.
The information that is downloaded will just be the payment info. Yes, it is possible that some of your account info will be downloaded on the backend as it may be needed to verify you and allow the download.
How do I Import Income from Square?