Getting lots of backlinks suddenly to your website could harm your SEO.
Is it a good idea to invest in link acceleration? Should you want to increase your backlink velocity (the rate at which other websites link to yours)?
Generally NO. Be suspicious of any claim to get you tons of links quickly. These tend to be low quality, or even spammy or malicious, links that will hurt your SEO due to both poor link quality and speed of link acquisition.
This is interpreted by Google as an attempt to manipulate your search engine rankings for your website, to trick Google into thinking, "Wow. With all these links going to XYZ website, it must be an authority on a topic, or a source of news about a trending topic." But Google is hip to such black hat gimmicks.
Goodroi gives a good explanation of Link Velocity in Webmaster World thread.
I would guess that the more links you have the more links you can gain. The New York Times gaining a thousand links overnight is not a big thing. A brand new 20 page site gaining a thousand links overnight is a big potential red flag.
I would also suggest that not all links are equal. I suspect some links are high quality and other links are very poisonous. If you gain a small number of very poisonous links from websites that obviously exploiting Google, I would expect you will have ranking trouble sooner than later.
I value links by the odds that the link will send me real traffic that converts. The more chance the link will perform, the more effort I exert in developing that link. My focus is building up external traffic sources so I am not dependent on Google. The more I do this, the more traffic Google sends me. People that tend to target low quality links that don't send any traffic tend to have more ranking issues IMHO.
In a Google forum, this was the Best Answer (by RainboRick) to a question about link velocity.
Google employees have occasionally indicated that when a site suddenly gets a burst of links, it can be taken as a sign of attempts to manipulate the rankings. But this is in the context of a manual review or a situation that might trigger a manual review.
Since a page about a hot topic might well see a sudden surge of links, it isn't automatically going to damage a site's rankings in and of itself. But if the links look like they're artificial in some way, they could become a problem.
Generally speaking, this shouldn't concern most webmasters. Sites go through peaks and valleys of link building, especially when they're new.
As long as you're not out there buying links or getting a lot of site-wide links from unusual or unrelated sources, it shouldn't be a problem.