This will most likely require regularly paying in order to keep the same number of members (or to show a false growth) in your group. As probably only 10-20% of the people will stay, you'll have to pay every now and then for 1k more members. If approximately 20% out of 1k stays, that's $250 for a thousand staying members. But even out of these, a lot may leave in time.
The same goes for Instagram. If you want to falsely grow an Instagram account, you'll have to regularly pay for it or it won't work.
But the little calculus above is imo the best scenario. If your invited members are completely uninterested and unrelated to your group, expect under 10% of them to remain. Big loss for a shit ton of money.