Should I spread the pads out on the footprint of a THT LED?
Most professionals here will tell you not to buy a product without a datasheet, and that's good advice. On the other hand, most "generic" products are similar to properly documented products (perhaps with greatly relaxed performance). In this case, I think it's similar to the Kingbright part shown here: 



You can make measurements (with calipers and/or micrometer preferably) to confirm or disprove that hypothesis. So let's say this is the 
actual part. 

I would say this is a bit close, but possible, depending on design rules, the below is 2mm x 0.8mm pads which results in 10 mil spaces (0.254mm) and 0.1mm annular ring, which is probably okay. 



Whatever you do, you should not push the LEDs all the way down to the board, as that will stress the epoxy and may result in failures. The Kingbright LED has a leadframe feature that will stop it from being pushed all the way down, but you can also use a spacer or a jig.