The 5000 was merely a nice round(ish) number that I picked from thin air. I just used it to attempt to illustrate the point I was attempting to make. The influx would affect numbers by either offsetting them, negating them or completely undoing any progress made. This, as you pointed out, would affect percentages. And, yes indeed, we are including those immigrants who are currently in custody (i.e., being held and processed) in our overall vaccination numbers. Both in overall (raw) numbers and approximate percentages.
I'm not entirely sure how to get that point across any better but I hope I succeeded.
The method by which immigrants enter the US is vitally important actually. As America is a Constitutional Republic... we're a nation of laws. To enter illegally displays a basic misunderstanding of what America is. Not sure how pointing that out is a virtue signal though.