Purchased MLP units late in the year but there were no distributions for me in 2018. Should I wait for the K1 or can I assume: no distributions, no tax owed?

It might be hard if you're expecting a refund, but you should always wait.  The IRS's computers are looking to match what the LP reported concerning your tax ID (SSN) with what you report came from the LP. There may be some non-taxable information that the LP reports to the IRS that is included on your K1.  Could be something irrelevant to you. Always think in terms of computers. The IRS vs. Intuit (TurboTax)

Its called the "matching program". The IRS computers look to match what a "3rd party" (employer (w2), investment company (1099-Div, etc.) reports to them, with the tax id (SSN) of those affected. It's pretty much their number one way to verify what your "reporting" is correct.