If these soldiers were already believed innocent under US military law? And the ICC wasn't willing to play ball?
Then at least an investigation has taken place under the terms of the UCMJ; which means the US authorities are aware of the facts; which means they are aware of the chance that other jurisdictions, namely the ICC, might be interested in delving in deeper; which means the personnel won't be deployed abroad, at least not to signatory countries.
Also keep in mind that the ICC is chiefly, if not solely, interested in the top decision makers, politicians and generals. They don't waste time hunting the small fry. Recent history shows that US junior officers, NCOs and privates can engage in war crimes - on their own initiative and generally against orders. To find a US general who issues criminal orders and makes those a standing policy, you'd need to go back to 1901.
I'm just curious about the consequences of it actually happening.
A. "It" meaning that the ICC issues a warrant against US service personnel in say Germany?
If that's what you mean, the consequence is that some German has a quiet word with somebody in the US embassy, and the personnel involved just happen to be redeployed to the USA before the Polizei knock at their doors.
B. "It" meaning, OTOH, that the personnel are already detained somewhere in Europe and the US Administration does order such a folly as a special forces raid? If so, that is a covert operation. Then the consequence is that the shootout is reported as a terrorist operation by some local faction that wanted to avenge the alleged crimes. The personnel disappear, never to be seen again. They actually change identities and live in the USA heartland, but the version above spares embarrassment to both the USA and the targeted country, say Germany.
Relations between the USA and Germany cool down for a while, but then Realpolitik considerations overcome that. The Germans learn that next time, the option they should choose is A., above.
All that is assuming both that everything goes to plan and that the lid can be kept on the folly. If the operation fails and is therefore disclosed, or if it succeeds but it is nevertheless disclosed, then, well, I won't venture to assess the consequences of that.