but what I'm really asking here, does the site actually work?
Sure, there is nothing stopping it except math from stumbling across a funded private key. I suspect that if you did, a script somewhere on the site would automatically import the private key and sweep the coins before you could, though.
in other words if I'm super-super lucky will the site show an actual wallet with funds?
It could, but you are almost certainly underestimating just how super-super lucky you would need to be. We are talking in excess of winning the lottery 10 times in a row lucky.
Also what are the odds that the first and last few pages contain wallets with "tx" in them and 0 balance, is it a coincidence?
They keys are not arranged randomly. What you are seeing is private keys in the WIF format, which is converted from the standard HEX format of private keys. The first key which shows 99+ transactions (5HpHagT65TZzG1PH3CSu63k8DbpvD8s5ip4nEB3kEsreAnchuDf), when converted to HEX, is:
0000000000000000000000000000000000000000000000000000000000000001
Someone has obviously picked this private key manually (which is incredibly stupid, but some people do it). You can see the same with other private keys of certain patterns. For example, the private key:
1111111111111111111111111111111111111111111111111111111111111111
Leads to the address 1MsHWS1BnwMc3tLE8G35UXsS58fKipzB7a, which also has some transactions.
I think the site is a fraud and just try's for people to enter their own private key in the search to see which page they're in.
Correct.