In the vast majority of districts, yes, the 1st and 2nd most-locally-popular candidates would be elected.
In other districts, the 1st most popular candidate would be elected, and the 3rd or 4th-most-popular candidate. This would likely happen only in those districts where there was little difference in percentage support between the 2nd, 3rd and 4th candidates, and is an effect of the mathematical algorithm that is used to determine proportionality.
It is worth noting that in either scenario, more voters overall are satisfied than under the current system, in which only the 1st-placed candidate is elected, in a 'winner take all' scenario. Under this current system, all the voters for other parties are unrepresented.