He scouts them. He's likely willing to draft them. Rumor had it they were very high on Porzingis in 2014, but he withdrew from the draft. They also supposedly would have taken Saric in 2014 had he fallen to 17. Obviously he couldn't get Porzingis in 2015, but some rumors were that he was trying to trade up for him.
International players carry an extra risk because they are typically under contract internationally, which can delay their arrival. During the height of the big 3 era, it made more sense to have someone who was ready to come immediately, and hopefully at least play a bench role, rather than waiting years to buy him out of the contract. Additionally, in the prior CBA teams weren't allowed to pay anything for an international buyout -- it all had to come from the player's rookie scale contract. Given that the C's were picking in the 25-30 range many of those years, that meant rookie scale contracts were of low value, which further contributed to the likelihood the pick would have to delay his arrival until his contract expired.
I do think the early version of Ainge the GM missed out on international players a bit, but I think the current version has no hesitation. They simply haven't been the top player on his draft board when the Celtics were on the clock.