yeah, had a crude spread spectrum system once, and as one pseudo random modulated it (BPSK), you could see a tiny hump at the carrier frequency...LO leakage thru the mixer. I did finally figure out a cute way to remove it...but not so easy.
It gets more important for low level systems. Like you are piggybacking modulation on a satellite repeater, but your spread signal is under the thermal noise floor. You can share the repeater channels ONLY IF there are no discrete higher level spurs leaking out...like a tiny hump right at the carrier frequency!