That is a interesting question.
When experiencing a brand across multiple touchpoints it is important to ensure consistency. Variables tend to break the experience.
You want to evaluate the creative of the user journey. From Advertising or Email to Landing Page to Final Destination. Are they all using gradient treatments? If so the buttons should always look the same and be instantly recognizable.
Running a test on gradient vs flat is very much like testing green button vs orange button.
The most important things to remember with buttons are contrast and affordance. You shouldn’t encounter button related conversion challenges if you adhere to the above mentioned.
Here are two articles that can help by Oli Gardner.
A breakdown of affordance as a design principle.
Read the Call To Action section of the article.
And here is a simple tip by Michael Aagaard
I would suggest investing in a test that would give you a higher return.