I don't think they would. A declaration of incompatibility affects nobody except the UK government. The purportedly incompatible law still stands and must be obeyed, regardless.
Then it's up to the UK government itself to either change the law, if it accepts the declaration, or appeal it, if it thinks the law is good and wants it to stand.
I don't see how that affects FWS. I doubt whether they would even have standing to appeal a declaration of incompatibility.
For sure, the court will only grant a declaration of incompatibility if FWS win this judicial review, an outcome of which will be a requirement to change the policy, so it would actually be a victory of sorts.