I don't think gs does this (at least on linux).
I tried it running from to my linux box from a SSH session and switched focus to the X11 windows that pops up with the rendered image (tiger) and the keys I pressed there did NOT go to the application on the remote host.
The (end of the) strace shows GS waiting for stdin -- the read with fd=0
read(3, " } if\n psuserparams readonly p"..., 4096) = 3258
brk(0x1124000) = 0x1124000
read(3, "", 4096) = 0
close(3) = 0
munmap(0x7f8ccaee5000, 4096) = 0
poll([{fd=4, events=POLLIN|POLLOUT}], 1, -1) = 1 ([{fd=4, revents=POLLOUT}])
writev(4, [{"+\2\1\0", 4}, {NULL, 0}, {"", 0}], 3) = 4
poll([{fd=4, events=POLLIN}], 1, -1) = 1 ([{fd=4, revents=POLLIN}])
read(4, "\1\1'\0\0\0\0\0\1\0\200\0\0\0\0\0\1\0\0\0\264\2\0\0008\0A\2\4\0\0\0", 4096) = 32
read(4, 0xc9bd54, 4096) = -1 EAGAIN (Resource temporarily unavailable)
fstat(1, {st_mode=S_IFREG|0644, st_size=143204, ...}) = 0
mmap(NULL, 4096, PROT_READ|PROT_WRITE, MAP_PRIVATE|MAP_ANONYMOUS, -1, 0) = 0x7f8ccaee5000
write(1, "GS>", 3GS>) = 3
read(0, ...unfinished ...
I had to switch focus back to the ssh window in order for the key press (Ctrl-C) to take effect. I had tried "quit" as well as ctrl-C when the focus was the image X11 window.