I’ve never seen anyone verify a millisecond number of latency caused by the HD Box Pro and it’s something I’ve wanted to do for a while and is on my list of things to do.
I have roughly 10 HD Box Pro v2 from China and 10 Monoprice HD Box Pro v1s and have used them at events here in the AZ community for roughly 2 years on PS2/PS3/Wii systems for both casual and tournament gaming.
I’ve had good reviews from many people within the AZ gaming community including one of the state’s top notch 3rd Strike players said3s (Abe) from Arcade in a Box on a PS2 as well as Juicebox on SSFIV on PS3 and Haz from team hAZmat and others Marvel3 with the PS3.
As long as they’re set in specific settings resolution wise I believe they’re under a frame of lag (+ whatever you get with your monitor) but as I mentioned I haven’t done any OFFICIAL tests other than the VGA passthru.
I did a fairly lengthy detailed writeup on them HERE on the Shmups Forum and plan on testing them as soon as I get my VH236H Evo monitors in the mail and my buddy lets me borrow his Sony Trinitron CRT component input monitor.
As soon as these tests are done I’ll be sure to post the official results for people to view/argue. 
I was NOT aware that they would be capable of handling any 240 signal though. I know they handle any PS2 game (even those that don’t support 480p) as long as the output on the PS2 settings is listed as component cable and it’s hooked up.
Anniversary Collection works just fine on PS2.
-FrankCastleAZ