No, for several reasons.
There is no sister site about immigration. I assume you're thinking about Expatriates, but that's about expatriates, i.e. people who are living outside their own country, not about immigrants, i.e. people who are changing countries.
We get very few questions about immigration. We get more questions that are relevant to expatriates, but most of them are on-topic here, and questions that are on-topic here should not be migrated. Questions about border crossings, for example, are about travel regardless of any consideration about visa status. Other examples I remember (but didn't keep the links, sorry) include buying a car abroad or opening a bank account (which Expatriates would reject because “you have no intention of moving [there]”).
In any case, tags are not intended to create ghettos, nor to tell something about what should be done with the question. they're intended to indicate what the question is about. If a question is about immigration, tag it immigration. If not, don't tag it. That's only very loosely related to whether the question is about travel (on-topic) or not (off-topic).