Can a Bitcoin block be less than 1mb? Can a Bitcoin block be less than 1mb? 

To my understanding, a miner receives broadcasts. However, if not enough transactions come in, then would it just prematurely hash the block?
Yes.  Let's calculate the minimum size of a block:


The block header must be exactly 80 bytes.  This is the only part of the block that miners actually mine; the rest of the block is data that the header securely references.
The transaction count.  This isn't part of the block header and it isn't part of the block data, but it's part of the peer-to-peer protocol block message so it gets counted towards the block size.  For blocks with 253 or fewer transactions, this is 1 byte.
The coinbase transaction, the only required transaction in a block.  The coinbase transaction has the following fields with these minimum values:


4 bytes -- version field
1 byte  -- number of inputs (always 1 for coinbase transactions)
32 bytes -- outpoint txid; always 32 0x00 bytes for coinbase transactions
4 bytes -- outpoint index; always 4 0xff bytes for coinbase transactions
1 byte -- number of bytes in coinbase field (input script); always 1 byte for coinbase transactions because there's a 100-byte limit
4 bytes -- block height as a data push; required by BIP34
4 bytes -- sequence number
1 byte -- number of outputs, we're not going to have any (making the block reward and transaction fees paid in this block permanently unspendable; no real miner would do this)
4 bytes -- locktime
Total: 55 bytes



Total minimum block size: 80 + 1 + 55 = 136 bytes

Practically, the smallest reasonable blocks are in the 180-byte range.