It depends, but the answer is probably not. Most people operate shortcodes through an aggregator (OpenMarket, mBlox, Ericson IPX) that has direct binds to all the telecom carriers in a given country.
For the most part, aggregators charge a monthly fee usually tied somewhat to system throughput. For example, OpenMarket charges $1500/mo for 10 messages per second outgoing and $20,000/mo for 100 messages per second.
On top of that, they charge for messaging. Rack rate in the US is often $.035 outgoing and $.005 incoming. At Twitter's scale, they're probably paying a fraction of a penny per outgoing message and have most incoming fees waived. Some of that is carrier specific however. T-Mobile often doesn't waive the incoming message fees.
No, there are special plans for that, but also in a lot of countries (Italy for example) we never pay for receive sms or calls, so they could have a foreign plan (very common). Anyway, they may have a server that handle the traffic of the sms, and that is costing money for sure
For the most part, aggregators charge a monthly fee usually tied somewhat to system throughput. For example, OpenMarket charges $1500/mo for 10 messages per second outgoing and $20,000/mo for 100 messages per second.
On top of that, they charge for messaging. Rack rate in the US is often $.035 outgoing and $.005 incoming. At Twitter's scale, they're probably paying a fraction of a penny per outgoing message and have most incoming fees waived. Some of that is carrier specific however. T-Mobile often doesn't waive the incoming message fees.