Link popularity is definitely a factor (and it could help or hurt you), but with AV's use of the term vector dabase (themes) it's kind of hard to tell exactly how much of a factor.
Also just by comparing numbers of incoming links to a site, you can't accurately determine link popularity. With the use of the term vector database altavista can easily tell the difference between relevant and non relevant links and then filter out the nonrelevant links when determining link popularity.
I have not seen the stringent requirements for a base number of links like Google and Inktomi so pages withough link pop will rank OK to very good if designed well. I don't think it is a huge part of the algorithm, I have worked on increasing relevant links (after already having a decent amount) for customers and not seen a huge change. There are levels of boosting but I think Brett could help you more with that than I.
I've maintained it is worth about 10 ranking spots from about page four to page 10. Above page four (position 40), I would argue that it doesn't matter at all. There really is a boost down there in the lower ranked pages. We saw it with the last buddy links refresh where people just zoomed up 10 spots, but they were all pages down below page four. People that were on page 1-3 were wondering why nothing happened with those pages - there was no benefit there. I think they are just using it to see if a page is 'top 100' worthy. If a page has some linkage, even a little, it makes it past that first cut off point and gets you included in the main show. It won't boost your rankings when you are already up there because I don't think it is actually used in the 'final algo'. It just increases your 'dead score' while setting on the db doing nothing. What I feel Alta is doing, is actually grading pages as they are spidered. It gives them the altavista quality "thumbs up/thumbs down" rating. It first runs through the spam checks, then it looks for dupes, and then finally it gives it a rating based on the rest of the site (cough - this is the them'ing stage). After that, it is up to the page to live or die in the rankings. Linkages gets you in the door, but the page still has to perform.