Saints Row 4 is a small game, originally a 360/ps3 title, they can fit it on an 8gb card. SR3 didn't require a download so I see no reason why this one would either.
I swear Saints Row 3 on Switch in Australia the advertising preorder box said required SD card for download. This is the reason I didn't buy it. In fact I recall even cancelling preorder based on this.
Maybe a big screw up in advertising? or in Australia we got screwed?