Not really, so why should they have bothered to implement it, as doing so would have needed to add at least one (more like two or three) additional ROM entries (*3).
When it comes to the 'illegal' opcodes (*3*4) it helps to differentiate between the 'tamed' ones and the 'wild' beasts. The differentiation becomes quite obvious when looking at the opcode chart:
(Taken from Norbert Landsteiner's 6502 "Illegal" Opcodes Demystified page - with some colouring added (*4*5))
There are two exceptions to this, $8C SHY abs,X and $8E SHX abs,y (*5*6)
The read ones, mix up functionality from other groups as their group (CC=11) is simply not decoded at all. They are the real orphans of the 6500 design - and like orphans they look for surrogate parents in group CC=01 and 10 (*6*7).
*3 - It would at least need to suppress the increment of the PC, like done with a NOP, during the second cycle, followed by the store and an increment after the store, so maybe 3 additional lines or ~2.5% additional ROM for an instruction with rather dubious usability?
*4 - Naming is a real crux here, as the term 'illegal' implies something that not really exists in an instruction set. Opcodes not defined to carry out some operation (aka 'unused') are simply that: Undefined/Unused Opcodes.
*4*5 - Norbert Landsteiner's page goes way beyond listing the 'illegal' opcodes, but dives deep into the structure, following Neil Parkers well known The 6502/65C02/65C816 Instruction Set Decoded
*5*6 - Personally I would see them as leftover/unfinished implementation of STY abs,X and STX abs,Y, but that might be a different story.
*6*7 - I know that this is due the way that the groups are decoded into three select lines within the decoder and 11 simply activating the group 1 (CC=01) line as well as the group 2 (CC=10) line. adding one gate here could have prevented all of that and saved us all the hype about 'secret' opcodes and so on.