Getting to many links all at the same time can harm rather than help you in the search engines, not only does it not look natural to Google to have a ton of new links suddenly appear to a site that the month before was not getting any links or whose link acquisition has been steady for a period.

There can be legitimate reasons for a sudden increase in links such as the launch of a new site or new product or something that has been picked up by the news media or bloggers sphere that has been discussed a lot and commented on.

This needs to be taken advantage of and the link spike needs to be continued so that the level of links coming into the site remains high but the spike flattens off.

If this is done properly with links pointing deep into the site the number of pages that Google will list in the index for your site will increase and not drop as pages fall out of the Google listings.

The more pages you have in the listings the more chances you have of ranking well for a variety of key words related to your business and there for the more chances you have of  attracting visitors to your site.