Approaching people in chat to talk about Area51 proposals is fine. But you need to turn your message around and focus on education and taking ownership of the proposal, and not blaming them for not voting.
The problem with your idea
Your choice of phrasing could be interpreted as borderline annoying and approaching rude. From your example (emphasis mine):
@XX I recently noticed that you have followed Arts and Crafts proposal but haven't used your votes. I request you to use your votes on that proposal since it will help the proposal to move to the commitment phase. That proposal still needs 7 more questions with 10 votes to move forward. Thanks.
The 2 bolded items are what I have an issue with.
I request you to use your votes - You should not be telling people where and how to vote. It is possible they voted to abstain from further voting, which is a vote in of itself. Also, I know you said "request" here, but it comes of in a very commanding way, so it seems like a directive.
That proposal still needs 7 more questions with 10 votes - While you don't say this explicitly, by focusing on the number of examples that still need 10 votes, you come off as you are encouraging people to vote up questions just to get the proposal to move to the next stage.
The entire message also comes across a very accusatory because you are putting some level of "blame" on them for not voting.
A potential solution for new users
Rather than focusing on telling the user what to do, you could think of a better way to approach this. Education is a good start, especially if the user appears to be new to Stack Exchange and to the Area51 process.
@XX I recently noticed that you have followed Arts and Crafts proposal but haven't used your votes. Did you know that you can freely change your vote without any issues, so it isn't necessary to "save" your votes for later questions. If newer questions come in, you can just unvote a previous question to vote for the new one. The proposal is getting close to the next stage of the evaluation process, so you won't be able to vote once we get there, and using your votes is critical to getting to that next stage.
I actually started with the idea of being able to freely change your votes because I was lightly watching 2 or 3 proposals before I realized that I could change my vote without it getting locked in after 5 minutes. Once I learned that, I tended to vote more freely. I also focused on the voting being crucial to moving to the next phase without harping on the number of posts that need votes.
A potential solution for experienced users
The other thing to keep in mine here is you want to pay attention to the user's level of activity on Area51. If they are involved in other proposals and have been through the entire commitment process a couple of times, it is likely that your original message (and even my suggested message) would come off extremely rude since they should know how the process works. So for the experienced user, I'd think you should have another different message, focusing on the questions rather than the votes:
@XX I recently noticed that you have followed Arts and Crafts proposal but haven't used your votes. Are there questions or topics you would hope to see on this site that have not been posed as examples yet? I am trying to move this proposal forward, so if there are topics missing that you'd like to see, I can help with putting some more example questions out there.
Now you've turned this into a "what can I do to make it easier for your to use your votes" rather than blaming them for not voting.
Final option for everyone
Rather than one or 2 canned messages, Lance's point is a very good option - just approach it more informally. Talk to them about the proposal in general. See what they want from it and why they are following. Talk about the example questions and the idea of voting can come up naturally in the discussion.