It is not in "the" ethereum spec, so no. But it is a feature that has been discussed for "ethereum 2.0" or similar. It is possible that there may even be a hard fork that will enable it in the then-existing network, but there are none currently planned.

This feature can be easily realised outside the Ethereum virtual machine (and thus keeping the VM simple): Create a (reusable) contract where contracts can register to be called at a certain time (and provide a reward as compensation for the gas costs). A script can poll this contract from outside and call it at the appropriate times. The contract could be similar to the following.

contract CallbackRegistry
{
  struct Entry { uint time; address addr; bytes data; uint reward; }
  mapping(bytes32 => Entry) entries;
  function register(uint _time, address _addr, bytes _data) external returns (bytes32 _hash)
  {
    _hash = sha3(_time, _addr, _data);
    entries[_hash].time = _time;
    entries[_hash].addr = _addr;
    entries[_hash].data = _data;
    entries[_hash].reward = msg.value;
  }
  function invoke(bytes32 _hash) external
  {
    if (entries[_hash].time > 0 && now >= entries[_hash].time)
    {
      msg.sender.send(entries[_hash].reward);
      entries[_hash].addr.call(entries[_hash].data);
      delete entries[_hash];
    }
  }     
}

The simplest way to do it is using Ethereum Alarm Clock. It's on mainnet and integrated in MyCrypto wallet. Here's tutorial to accomplish scheduling based on block height / timestamp, as you mentioned in the question: https://medium.com/@MyCrypto/schedule-your-ethereum-transactions-now-on-mycrypto-92a6305f7dcc.