The TIL311s take a 4 bit input (that would be between $0 and $F hex) and display the hex value.
The KIM/PAL has seven separate output lines that the ROM (and other software) turns on (or leaves off) as needed to display whatever is desired. There is a table in ROM that translates a hex value into the combination of seven segments needed to display the hex value.
The KIM/PAL also continuously refreshes the display as it polls the keypad for input. If you jump to some code that doesn't explicitly keep the display "on", it will blank. That is different than latched output like the TIL311 where you put the 4-bit value you want in, strobe the latch line, and the display holds the value until you either strobe or blank it.
Since they are fundamentally different, you would have to rewrite the ROM code. Getting the right character for the right value would probably be fairly easy--you just would map $0 to $0, $1 to $1, etc. and use 4 bits of the 7 that are available for output. (You could probably even skip the lookup table and free up a few bytes that way.) You would have to handle the strobe signal which could be done with one of the 3 unused lines I suspect. (And maybe use another one to allow blanking.)
You would not be able to run any of the original code that drives the individual segments.
From a "wiring it in" perspective, it probably isn't overly difficult. (You would need to figure out an adapter circuit for the TIL311 to the wires used for the seven segments.) The software probably wouldn't be overly difficult either since the ROM source code is published. (There are only a few dozen lines of assembly code associated with driving the display.) The end result would be "one of a kind" and not compatible with anything that uses the display beyond calls to the ROM routine. (So things like Hunt the Wumpus or most stuff from the Book of KIM isn't going to work.)