Yes, "CO2 juicing" will help.
You can cause an infestation via lowering the CO2, adding it intermittently etc.

If you keep doing that for sometime(weeks typically), you can induce BBA.
This is for higher light, well planted tanks that are doing well anyway(a control tank basically).

Hair will go away on it's own, I'm not sure why specifically however, but based on good CO2, inducement, it seems to respond well to CO2 changes, slightly poorer nutrient levels for the plants.

So over grown tanks, lack of pruning etc can cause this, CO2 declining........., leaving for a week or two without dosing/pruning, I've found hair algae in each case to appear. Smaller tanks with CO2 issues etc also.......I had a diffuser that just would not give me consistent CO2 and I never had issues in an identical tank with another good diffuser.

So some CO2 related mechanism seems pretty likely for a cause.
Excel might get rid of it for that reason(carbon addition if it was low via CO2 gas), rather than as an algicide........
Plants seem to perk up, start over growing the algae, pruning it out, and it goes into spore phases and the adults slowly die out.

Similar thing happens with BBA, takes longer and is more of an issue for many and BBA is much less limited by nutrients/less affected. Cladophora seems to like somewhat leaner nutrients.

In an ADA sediment tank, this is less likely to occur, but still can certainly......but then it's more CO2 related exclusively. With plain sand etc, flourite etc, you likely need more ferts as well.

Regards,
Tom Barr