No, the local oscillator frequency varies all over the place--it is 10.7 MHz above whatever frequency is being tuned. So on a standard FM radio, the LO frequency could be anywhere between 98.8 and 118.6 MHz.
The local oscillator is just an unmodulated carrier. When mixed with the intended station (on whatever frequency) the result is a modulated signal on 10.7 MHz inside the receiver. If you wired a shortwave receiver antenna into the IF circuit of a FM receiver, you could tune the SW to 10.7 MHz and hear that resultant IF signal. Same with AM radio--if I tune a longwave receiver to 455 kHz and place it next to an AM radio, it will pick up whatever is being tuned on the AM radio. But the LO is still just an unmodulated carrier. The resultant "difference" frequency is what has the modulation, and it does not change.
Or a bit more if the station was running SCA at 92 kHz.
The digital sidebands for HD radio extend out to 200kHz either side of the center frequency. These can actually be from a separate transmitter from the main FM station. If you look at a HD FM signal on a spectrum analyzer you can see the very sharply defined region where the digital sidebands are, plus the main signal, stereo pilot, stereo L-R subchannnel, RDS, and 67 and 92 kHz SCA. The sidebands can swamp a weak first adjacent FM station, although only FMDX geeks would care about that due to the poor signal.
But the LO is still just an unmodulated carrier--no HD present. If a LO signal is close enough to the frequency of a desired station, yes, it could overwhelm an HD sideband if the receiver's IF bandpass is wide enough. But HD does not increase interference from LO's--it is just a victim of those LO's.
OK, time out. I'd really like to put this thread on a little higher level. I mis-spoke, probably because I was in a hurry. The IF doesn't move, it is 10.7 MHz. The LO is a single frequency, it tracks the RF 10.7 MHz higher. I've known how a freaking superhet works since I was 12! So no more of insulting denegrations, PLEASE!
Now back to the issue at hand. Can an IF image jam HD? There is a reason why the FCC established 10.6 and 10.8 MHz protections. Taking a Houston example - with a 200 kHz channel assumed (analog no HD). A radio tuned to 96.5 produces a LO of 107.2 MHz. So 107.1 (channel 107.0 to 107.2) and 107.3 channel 107.2 to 107.4) are not allowed within a certain radius, because they could potentially be jammed by the LO of a radio tuned to 96.5. And Houston has no 107.1 or 107.3. It does, however, have a 106.9 and a 107.5. Those are 300 kHz away from LO's of nearby radios at 107.2. They will not be jammed.
Now add HD to the equation. The HD sidebands of 106.9 overlap 106.7 and - drumroll - 107.1! Similarly, the HD sidebands of 107.5 are on 107.3 and 107.7. !07.1 and 107.3 are the exact frequencies disallowed by FCC protections. Oops! So - depending on how wide you think the entire bandwidth of an HD FM station is - there is a real potential that part of the HD bandwidth for 106.9 shows up on 107.2, and the same with 107.5. That is what I think I am experiencing when a car drives by or catches up at a light.
I first noticed this when the weather was nice, and I think it was somebody listening to classic country on 97.1. My HD on 107.5 dropped. Because it was HD-2, and both of us had windows down, my radio went silent and I could hear his radio. I heard an ID on his radio. We were at a light. When the light changed, and he went ahead, my HD came back. I caught up to him at a light a mile later, and sure enough my HD went out as I got near his car. It didn't dawn on me what was going on at first, because it didn't make sense. But when I realized - the LO of 97.1 from his radio is 107.8. And an HD sideband of 107.5 is on an adjacent frequency of 107.7 - depending on how wide that sideband is, it could be on 107.8. As time went on, I began to get additional examples affecting primarily stations above 98.5. You commute the same route every day, and start to see the same cars. The same cars cause HD dropouts.
I really think there is an issue here with the LO of neighboring cars radiating and jamming my HD. It is particularly annoying because I pretty much only listen to HD-2, and it goes silent. If it is a 2 minute light, that is half a song! I seriously doubt the HD engineering "geniuses" thought the implications of using adjacent channels through carefully enough.
Like I say - don't take my word for it. Try it yourself! Two cars parked beside each other in a driveway, one with HD. Try to jam HD by tuning 10.4 to 11 MHz lower. You can! I can do it dependably in my driveway. The HD sideband power is low as it is, it doesn't take much to zap it.
