The brief answer to the above question is evidently "No." The background, explanation and evidence are below.
The Google Search Engine Results Page (SERP) position of a Web page is determined in part by the number of links to it with a relevant keyword. Thus, a page about Widgets that has 1,000 pages linking to it with keyword widgets will have a higher rank than a page with similar characteristics in all other respects, but which has only 5 links to it with keyword widgets in the anchor text.
A logical question and one that I have seen posed frequently, is whether a page that is returned in a high position for a given keyword can be demoted to a lower position for that keyword simply by linking to it with a different keyword. That would seem to be a logical possibility, and I have even seen posts where people present elaborate calculations of difference scores to show how the irrelevant links should affect the score. I brought this question up here: Can irrelevant link anchor text hurt page positioning?. People have argued about this point quite a lot, but I didn't see that anyone tried to test it. When I asked a support person at an optimization firm, it was evident from the reply that she didn't know either. Since I didn't know the answer and nobody was going to tell me, I decided to get an answer of sorts.
I decided to test it out using a Web page that I had previously brought to position 1 in Google for keyword Sexonomy. It is not hard to do that, since there are only a few hundred pages about sexonomy, despite the intriguing sounding name. Not everything to do with sex is "hot" it seems. As I had this page up there, used to prove a previous point about Search Engine Optimization, I could use it to test out this question. I generated numerous links to the Sexonomy page with keyword Mysterology. The result was that the page has (thus far) not moved from #1 place for Sexonomy, but it is now also #1 in Google for Mysterology, at least from this part of the world. Of course, this result may depend on many other things. My page may be so far ahead of the others for keyword Sexonomy that nothing will shake its position. Google may also apply a lot more filtering smarts to words that are frequently searched and commercially valuable. And of course, the Google algorithm might change one day real soon in one of those Google updates.
You can try the search and tell me if the same page is #1 for both keywords. Write to me at ami(dot)isseroff(at)gmail(dot).com