Suppose I’m feeling generous and I ignore the implications of the Euthyphro dilemma. If we put aside the fact we have no reason to believe goodness can come from a subject, not even god, would theists then be able to establish a system of objective morality? No.
When it is asked why humans ought to obey god one of the most common responses is that god is goodness itself but this response is nearly a nonsequitur, as it only tangentially has anything to do with the actual question we asked. Saying god is goodness itself, even if this is objective goodness, doesn’t answer why we ought to value this goodness and hence obey the duties imposed on us by god. At best it sidesteps the question perhaps in the hopes that it should be obvious that we ought to value goodness but it surely doesn’t explain why this is so.
It also should be noted this claim is often made in a manner which is unfalsifiable because no state of affairs exists which would count as evidence against the claim that god is goodness itself. Under such circumstances, where there is no possible empirical state which would contradict the claim, one would be no less justified in saying god is evil itself. So the statement god is goodness itself would lack meaning and I would have literally no reason to believe it. Of course, with no reason to believe god is goodness you can’t establish that we have any reason to follow duties that follow from the god being goodness.
Suppose instead the theist claims god is goodness means god is merely intrinsically good, by virtue of its nature, and that god can detect the objective goodness in reality. Would this then enable a objective moral code to have meaningful utility for humans? No, we’d still be in the same position with respect to discovering these absolute moral rules. If god is using a faculty we do not possess, and can not imagine, in order to assess the goodness of acts then what could possibly count as evidence that these moral realities actually exist? Even if some purely factual “is” at the “ground floor” of reality determines some “ought” without any means to verify this, even in principle, we’d still have no justification for accepting this is true. Literally nothing a god could do would even demonstrate that such a principle of reality exists let alone that any particular conclusion within such a framework is true. Sure a god could threaten us with punishment for not following its rules but such a threat would only be effective insofar as it appeals to our subjective value of not being punished. It wouldn’t clarify when, if ever, we should sacrifice our subjective account of morality in order to avoid punishment no more than the armed thief’s threat to “surrender our wallet or our life” does so.
Not to mention there’s little more obviously immoral, in my subjective opinion of course, than holding creatures to standards they are incapable of understanding. This is why we don’t punish cats or infants in the same way we do adults. So long as we attempt to place morality outside something with at least vaguely human attributes, both physical and cognitive, we will only push morality beyond human comprehension. Ultimately any system of morality that appeals to claims which are in principle unverifiable, like systems based on gods, is bound to fail.