Is "demonstratee" a legitimate word?
Solution 1:
Fundamentally, there's nothing that makes one word more legitimate than another, other than actually being able to use it and have your audience understand you, but I presume you want to know how widely accepted the word is.
A quick Google Ngram search shows that it's rare, but occasionally used. Looking more closely, many of the places where it's used appear to be typos, for example:
This is demonstratee by Figure 6, where twice dilution…
But there are occasional valid uses:
Nothing on the pacemaker or the defibrillator is connected to a patient [sic] or a demonstratee.
It is indeed a valid word, and there's nothing preventing you from using it. It's rare though, so depending on your audience, if you really want to avoid confusion, perhaps you should stick with simple common language and simply refer to the demonstratee as the object of the demonstration.
Solution 2:
But what the heck does it mean? I thought this through and came up with:
An employer is one who gives employment. An employee is one who takes that employment. By that token, a demonstrater is one who gives a demonstration, while a demonstratee is one who takes the demonstration (or observes it).
I think it is a valid coining, but only just barely. I think the tendency would be to say "audience member", or "observer". Of course "demonstratee" is precise.
But awkward and bizarre, IMNSHO.
Solution 3:
If it were me, I'd simply use a different word that is appropriate to the situation. For instance, if I were a clerk in a store and a customer wanted me to show them how to use something I was selling - say an unusual keyboard - I'd show it to them and simply refer to them as a customer, not a demonstratee. For example "I just showed that customer how to use the new MK1000 keyboard."