Simple answer

All images are stored on roblox's database. Like how you're able to get decals from a link, you can use that same method to get place thumbnails or even profile pictures. The link is like this:

http://www.roblox.com/Thumbs/Asset.ashx?format=png&width=420&height=230&assetId=[PLACE ID HERE]

this gets the place thumbnail which is in png format that roblox can use and gets the image which is 420 pixels wide and 230 pixels tall. You can't change that because that's the default size of place thumbnails. So for example if I use the thumbnail for the place ID of 2153126 then It'll be http://www.roblox.com/Thumbs/Asset.ashx?format=png&width=420&height=230&assetId=2153126. You can use this link for decal textures or ImageLabels and such. It automatically updates with game thumbnail updates.

Hope it helps!

Extras

Here is a link of all the Web APIs that are usable. Web APIs.

Edit

While there is no way current way to get Game Icons there is a way to get them from ROBLOX's database which is through inspect element. This is unusable in game though. And there is no documented way to do it. So the answer is no.