Yes, it can. God certainly fights his battles vicariously through His people. The theme of Yahweh's opposition to other pagan gods reappears throughout Exodus and the OT.
Thou shalt have no other gods before me. [Exodus 20:3]
If this is taken as one of Moses' primary themes, as its prominence in the Ten Commandments would suggest, such words of judgment are not incongruous in the least. And this is by far the only such judgement in the Pentateuch:
And Jethro said, “Blessed be the Lord, who has delivered you out of the hand of the Egyptians and out of the hand of Pharaoh... Now I know that the Lord is greater than all the gods...” [Exodus 18:10,11]
For the Egyptians buried all their firstborn, which the Lord had smitten among them: upon their gods also the Lord executed judgments. [Numbers 33:4]
God fought this battle directly in the Exodus. But then He commanded His people to continue the fight against idols on His behalf:
Thou shalt not bow down to their gods ... but thou shalt utterly overthrow them, and quite break down their images. [Exodus 23:24]
The carved images of their gods you shall burn with fire. [Dt 7:25]
You shall surely destroy all the places where the nations whom you shall dispossess served their gods, on the high mountains and on the hills and under every green tree. [Dt 12:2]
The epic battles of the Jews in the conquest of Canaan continued this ongoing conflict. The challenge between David and Goliath typifies it:
And the Philistine cursed David by his gods. ... Then David said to the Philistine, ... "I come to you in the name of the Lord of hosts, the God of the armies of Israel, whom you have defied. This day the Lord will deliver you into my hand ... that all the earth may know that there is a God in Israel." [1Samuel 17:44-46]
And of course, there was Elijah's challenge to the priests of Baal, and God's spectacular defeat of these priests on Mount Carmel:
“How long will you falter between two opinions? If the Lord is God, follow Him; but if Baal, follow him.” ... call on the name of your gods, and I will call on the name of the Lord; and the God who answers by fire, He is God.” [1 Kings 18:21,24]
Ones interpretation of Exodus (or any other passage) is not limited to a hypothetical "original" text proposed by textual critics. The final text as it has arrived to us, especially when taken in its broader context, has so much to offer to the interpreter.