My thought is they can't helped but be influenced. I remember a couple of years ago asking a NGC official at a show if the grades on PCGS slabs submitted for crossover were covered before they went to the graders. She said, "No". I must of looked surprised because she quickly added, "The grade on the holder won't affect them because they're professionals." I managed to get out of earshot before I burst out laughing. Cal
Professional - n. - one who is paid to do what he or she does. Don't put more into words than is there.
The graders are extremely experienced and know how to grade for themselves. Coins are graded by 2-3 separate people when submitted, and the graders can see the grade the others have assigned as well. So, even raw coins would be subject to this bias - if it exists. These guys know what they are doing.
While I can't speak to the degree of the influence, of course the assigned grade impacts them, we aren't moist robots after all.
Obviously IT DOES (good, bad and subject to "show around and tell" ); and the particular TPGS slab it is in does ALSO. If a TPGS does not cross certain other TPGS slabs then above does not apply. This is not true! However, the tier "head" or a "finalizer" can see the grades of others. I don't know if the QC graders can but I wish to find out as it makes sense that they would. In spite of this, each TPGS, and grader has standards and they should have no reason not to put what they think into the computer no matter the slab. In many cases though, it is best to send a coin in "raw."
