I get a lot of moisture in my ears from my hearing aids and I get a bad smell and have to use ear drops frequently. Would the Eargo help to prevent this problem?

I am familiar with Eargo and the idea behind it is to allow some ventilation around and through those little tendrils that cover the end of the hearing aid. It's a good theory and certainly may create less surface contact on the skin in the ear canal. As others have noted, your underlying problem may be a skin issue that needs to be treated. The challenge with the Eargo tendrils is that they can harbor infectuous cells from any skin or fungal infection. You'll have to clean those tendrils thoroughly and often in order to prevent recurrence.  A better option may be a slim tube or receiver in the canal device, both are small behind the ear models that offer MUCH better ventilation that in-the-ear or even behind the ear with custom earmolds. 

See an ENT about an ear exam and ask their advice on managing the moisture and the odor.  Then see your audiologist about whether an open fit device will work well for you. 

A cholesteatoma causes a chronic but scanty offensive smelling ear discharge. In the early stages, the condition is often painless and apart from the discharge, only an impairment of the hearing may be noticed. A cholesteatoma is a serious condition that needs immediate medical attention by an ENT specialist (otolaryngologist).

It could also be infection or some other problem so please see an ENT

If you have moisture or drainage from your ears I would recommend seeing your doctor or an ENT.  When you have an odor coming from the ear it could be the sign of an infection.

I'm not familiar with Eargo, but it sounds as though you have a fungal infection. It's best to have a medical consult with a physician or an ENT specialist to get a prescription for an antifungal medication - either drops or oral.