Yeah, it just means that the value of Y will depend on X, alpha, and beta. Nothing stops you from writing a “regression prior” like this:
X = pm.Normal('X', 0, 1, size=(100,3 ))
alpha = pm.Normal('alpha', 0, 1)
beta = pm.Normal('beta', 0, 1, size=3)
y = pm.Normal('y', alpha + X @ beta, 1)
You could then go on to use y in further computation. It might not be identified though, because there are infinite combinations of X, alpha, and beta that produce the same y. It’s hard to say more on that without domain knowledge, but just be aware that you might have to use quite informative priors on something like this.