Hope you are well. I have tested this out and yes QuickBooks Online will allow you to send an estimate/quote without having anything in the amount column.
Please see below the steps on how to create a quote in QuickBooks Online:
Step 1: Create a quote
Select + New.
Select a Quote.
Select a customer from the Customer dropdown.
If the work has already started, select a status from the Pending ▼ dropdown. This is optional.
Set the QuoteDate and the Expiration Date.
Enter the products and services you plan to sell.
Enter any other info you need.
When you're ready, select Save or Save and close or Save and send.
Please let us know if we can assist further.
Thank you,
Kay.
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