Lets triple that amount to 2800:).
And add another 1 million foreigners that will dig their way through the Swiss Alps , get one time machine and in 10 years you're going to ask yourself:
"What the hell happened to Switzerland !

"
Some 500 million plus people with Schengen visas and you are saying that just 1 million will climb the Swiss Alps? I think we can be pretty sure of at least 2 million from Romania alone.
The monetary reserves will run out in 10-12 months. After that we can sell the Swiss Alps, peak by peak. Once that finishes, we can auction parts of the Lake Geneva.
It will take just the first million to crumple the Swiss budget.
They will wake up only in a few months.
Also , just one million hitting their towns , imagine the picture with people sleeping in tents in parks.
London has seen this on a much smaller scale , and London is almost the same population as Switzerland.