Why, yes you can. With enough money, nearly anything is possible. (The Wall Street Journal talked about this a few months ago, back when my free time fell to zero, which was why I haven't brought it up until now.)
Here's part of the article:
"It isn't uncommon for a business book to land on best-seller lists only to quickly drop off. But even a brief appearance adds permanent luster to an author's reputation, greasing the skids for speaking and consulting engagements.... But the short moment of glory doesn't always occur by luck alone. In the cases mentioned above, the authors hired a marketing firm that purchased books ahead of publication date, creating a spike in sales that landed titles on the lists. The marketing firm, San Diego-based ResultSource, charges thousands of dollars for its services in addition to the cost of the books, according to authors interviewed."
Read the rest of the article here. It points out it's particularly easy to game business book bestseller lists, since even a few thousand copies can put you on a list.
I think it would be pretty hard to game any of the NYT's fiction lists. And I'm not just saying that because I've been on one. Given enough money, though, that still might be possible.
Smaller lists can probably be gamed more easily. Someone who had a lot of money (and who was also a good writer) once confided in me that she had gotten on the LA Times list through spreading around her own money to straw buyers who purchased the book.