According to VG Chartz the Nintendo GameCube sold 21.74 million units lifetime. 

As we all know, the Switch is riding a huge wave of momentum albeit with a current lack of AAA titles.

We all know the Switch will eventually surpass the GC but the question is when.....

The Switch is currently on 13.73 million units sold (according to VG Chartz) and selling heavily each week. 

Sometime in August probably.

I think maybe August, if Nintendo can keep up with the new releases

Like Pokemon Switch?

With it's current momentum probably around August or September

Probably around September, but it could be a bit earlier or later depending on the games that release.

This would mean that the Switch would only sell 7-8 million units in a year and a half time.

Before 2018 ends, maybe by november.

Switch was around 15m at end of December, it will be around 17-18m at 31. March, so it will pass GC numbers probably around July.

Agreed. Nintendo expects 2.9m shipped this quarter, which means 17.8m by the end of March. The next quarter should be at least a bit better since it actually has many first party releases, so let’s go modest with 3.5m. That would put it at 21.3m by the end of June, so it will definitely surpass it by July. And that’s a conservative scenario.