Yes, that's a good idea. So basically what you're saying is that I should wait to have the demo ready instead of contacting them first to know if they'd be interested. Sounds good to me.
Northernlion does Lets Plays of games of all varieties. He has upwards of half-a-million subscribers and prides himself on testing "the smallest indie games" to the biggest projects.
He seems super friendly, keen for variety and supporting small devs, and a reasonable reviewer. Unless I am getting my wires crossed, I believe he stated publicly that he doesn't tend to record Early Access / beta games because it's hard to give a fair representation of a WIP.
This is one person who I think has the right philosophy and is the kind of "approachable" lets-player you're after.
I believe he spoke about receiving requests, he claims to look at all of them and asked for people to be snappy with their emails; what the game is, who you are, a picture and a download link (something like that).
I think if you write a wordy letter, or talk about an unfinished game, you're not really giving a Lets Player any content to go on and they may as well forget you and go to the next email. Definitely keep it brief and only reach out when you've got something they can go on.