There are many essential oils and each can work differently and on different micro-organisms. They could affect the skin and mucous membranes in ways that are valuable or harmful.
For example steam-distilled eucalyptus oil is used as a primary cleaning/disinfecting agent added to soaped mop and countertop cleaning solutions, however there are hundreds of species of eucalyptus and dozens are used as sources of essential oils, so products of different species differ greatly in characteristics and effects and also the products of the very same tree can vary grosslywiki.
Some other studies show that tea tree oil is capable of killing MRSA in a laboratory setting, however there is insufficient evidence. A 2012 review by the NIH rates Tea tree oil as "possibly effective" for: treating acne, fungal toenail infection or symptoms of athlete's foot. Which indicates its antibacterial properties only against certain infection.
On the other hand some other essential oils generally should not be applied directly to the skin in their undiluted or "neat" form, as can cause potential danger such as severe irritation, provoke an allergic reaction and, over time, prove hepatotoxic. Some other, including many of the citrus peel oils, are photosensitizers, increasing the skin's vulnerability to sunlight.
In summary, non-therapeutic grade essential oils are never recommended for topical or internal use (including animals, which could cause extreme hepatotoxicity and dermal toxicity), unless specific essential oil has pharmaceutical properties and you know they're safe for use, however they're not good alternative to alcohol-based disinfectant products.