One voltage regulator (varistor?) instead of dozens of current limiting resistors in an LED array?
That will work, provided you meet a few criteria.


The current set must be less than the maximum allowed current in any LED.
The current set must be less than the fanout of your TTL minus the fan-in of all the gates you are driving. 
You must be willing to accept that when all of the LEDs are on, they will be much dimmer than when only one is on.
The current sink must have sufficient voltage compliance to work when its input voltage is equal to a minimum TTL high level minus an LED drop.


Items 2 and 4 are the big issues. Especially item 2. TTL is not real good at sourcing current, and it takes considerable input current at any input.

Frankly, if you're going to mess around with TTL (rather than something even remotely newer like CMOS, you're better off using an inverter/pulldown combination.







simulate this circuit &ndash; Schematic created using CircuitLab

This way, you have uniform loading on your signal bus, and uniform LED brightness. You can use something like a 74240 (or even better, a 74LS240 or 74HC240) as your buffer, and get 8 channels in a 20-pin DIP. You can use a 16-pin DIP pullup network, and get 15 pullups in a single package.