I would like to make the Expatriates proposal more popular and I wonder if it would be OK to share a link in several chat rooms. Would this be a spam?
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It would depend on the room's topic and your degree of participation in the room but, in general, yes. Its spam.
Different rooms have different standards for content and very different areas of discussion. If you were to interrupt an ongoing discussion, with an unsolicited link which is totally irrelevant, then it would be flagged and removed.
If the topic of the room or the ongoing discussion were to be related to the topic of the proposal, then maybe, just maybe, users might not consider it as such.
Also, it may be fine if you were to share the link in a room where you are otherwise active.
Area51 are part of StackExchange architecture, so spam isn't an adequate word. At worst case it would be off-topic post. Off-topic posts are something you shouldn't do anyway.
If you post it in appropriate room, I think it is reasonable. For example, many questions on Travel.SE are closed because immigration questions are off-topic there, so informing/reminding about such proposal is something absolutely about the site.
But posting it on programming chat would be inadequate.
Anyway, much better place to promote new site are the Metas of adequate sites. Expatriates proposal was announced many times on Travel.SE Meta.