According to the Sperry datasheet, "a keep-alive cathode provides an internal ionization source that reduces reionization time to less than 30us, allows zero supression, and improves the operation of the display in dark environments and at low temperatures". I'm pretty sure I read in a later Beckman datasheet that they are only needed to provide predictable operation in multiplexed displays (with blanking intervals).
On early Datron DMMs that use these same displays, the keep-alive cathodes are only used in the multiplexed display models (1051,1055,1057,1059), the static drive ones (1030,1041,1045) don't connect them.
Once the display has segments lit, the keep-alive cathodes become redundant, it's hard to say whether they are it is used / needed in the OP's unit (it looks static drive). It will start up at low temperatures and in the dark, just not instantly [Edit: It wouldn't anyway, the keep-alive is just another cathode].