It would not work. The issue is noise. Each piece of equipment adds some amount of noise to the image. One can transfer the information into the digital domain to avoid adding more noise, but the instant you do, everything that was below the noise floor or quantization limits of the digital medium is completely removed.
The noise floors and quantization errors which are acceptable are carefully tuned to the capabilities of the viewer. If the screen and surveillance equipment was designed for human eyes, you won't see anything out of the ordinary.
Now if the equipment was overdesigned, one might be able to see things. If you used multimillion dollar calibrated camera equipment, 24-bit/channel data, and a screen which was designed to actually be able to convey all of that content, then those with more capable eyesight might be able to see things. This is similar to how most people are cool with the sound that comes out of their crummy little earbuds when they play their ultra-compressed MP3s, while others can listen to their $100,000 sound system with studio monitors and the raw DAT tapes and tell you which recording studio the tape came from just by analyzing the sound. However, surveillance footage rarely comes from such high quality equipment.
Of course, you forgot the one person in the room who could pull information from the surveillance footage that nobody else could. Shame on you for not introducing him:
Sherlock -- See! There! When he held his watch up to check the time, you can see that the date is the 29th. You can also see that his watch is one hour ahead of all of the other clocks in the room. This could be attributed to carelessness, but note the attention he gives to the clock that is 1 minute ahead from all the others. Clearly this is not a man who makes such a mistake, ergo he is from a different time zone. But out of the 4,326 clock stores in the United States, none of them are close enough to a time zone border for a man such as this to not adjust his watch. Now look at his skin. Rough, dry, this man lives in a very hot and dry part of the country. Now, remember the date! It's the 29th of March! Daylight Savings! This man hasn't left his timezone, he's still in it! Arizona does not observe Daylight Savings, but Utah does! He's from Arizona, and visiting the only clock store within 8 miles of the border is Bill and Ted's Excelent Clock shop in Big Water, Utah. Our killer is there, now go out there and arrest him!
Never try to solve with nigh vision what can be solved by merely incorporating the clues in front of you! Deduction!