You can, but I don't think that you should unless you're getting some stupidly-low price on that GTX 1660 Super.
If you're buying new,
do not buy a GTX 1660 Super! I couldn't say it any more plainly than that. Just look at this ridiculous pricing:
MSi GeForce GTX 1660 Super Ventus 6GB - $230USD
The RX 6600 has 2GB more VRAM, is
35% faster (<-click to see the source of that number) and costs only $175USD brand-new:
ASRock Radeon RX 6600 Challenger D 8GB - $175 with a free copy of
Starfield.
This sale price ends in 15 hours but after the 15 hours are up, the price will only jump by $15USD.
Then the question will be "Can you fit a triple-fan card in your PC case?":
If you can fit a triple fan card in your case, get this one:
Gigabyte Radeon RX 6600 Windforce Eagle 8GB - $190USD
If you can't fit a triple fan card in your case, then get this one:
Powercolor Radeon RX 6600 Fighter 8GB - $190USD
Either way, you'd still get that free copy of
Starfield.
When it comes to the used market, on eBay, the GTX 1660 Super is
$130 which makes the NEW RX 6600 a better deal because it's
at most 46% more expensive for a card that is 35% faster, has 2 extra gigabytes of VRAM and is
brand-new with a warranty. If you decide to go that route, just remember to run
DDU before installing the Radeon drivers.
Unless you're getting the GTX 1660 Super for $75USD or less, I wouldn't buy it if I were you. Now, of course, it depends on where in the world that you are but even if the prices are different, the pricing trends themselves tend to stay the same around the world.