Absolutely! You could probably get a single rack to handle storage and broadcast of millions of tweets per minute, perhaps hook it up to a Teradata appliance to handle search and storage at that throughput. Throw it in a nice distributed database indexed by user. Then just another couple of indices for the hashtags and mentions, and the follows/follower graph. Throw in another few tables for handling API permissions, managing schema migrations while ensuring that data from day 1 is still as transparent as yesterday's logs, a highly replicated ad server hooked up to a realtime recommendation engine that analyzes an active user's current stream and recommends the most relevant ad (to maximize revenue of course), set up a few staffed policy teams to comply with the differences in global regulations, handle lawsuits and legal requests, and of course keep competing for more revenue with the likes of Facebook and Google.
It's pretty trivial.