Yes, you can.
Note: I have Pages and FileApp Pro, though. I don't know if that makes a difference.
For instance, I can search "color pages" in Safari then click "images", touch-and-hold on an image and up pops "save image" and "copy". I select Save... Then, back in Pages, I click the "plus" graphic in the tool bar and insert the downloaded image in my Pages document. I can't tell you how many file formats are supported...
Note that FileApp now shows the downloaded file in Photos & Videos. There is also a Files.. folder in FileApp. So, I assume most anything can be downloaded.
My question is, how do I select a linked file (csv) in Safari, that would be downloaded and I could open in Numbers?