FAI is referenced in clause 18.104.22.168 of AS9100 Rev D as an equivalent to “production process verification”. That is because the FAI process does a lot more than just validate the design, it verifies that all the processes, documentation and tooling utilized to create the first product are working properly to meet the design requirements. The FAI gives you a “line in the sand” stating, when everything was set up in this manner the product created meets the requirements. Design validation is making one article to show that the design can work.
In answer to your question, though, this greatly depends on how your customer has defined the FAI and design validation requirements. The FAI does show that the design works, but it also shows much more and a failure in FAI might be due to other situations in the processes and could give a false negative of your design validation. However, if your customer accepts this as a design validation then it could be acceptable.