No. Dr. Boom is summoned first. However, the "after summon" phase of the boom bots occurs first.
Dr. Boom hits board.
"Whenever" summon/play phase
Battlecry Phase
__Boom Bots hit board
__Boom Bots "whenever" summon phase
__Boom Bots "after" summon phase
"After" summon/play phase for Dr. Boom
So, it's a little confusing, but all of the summon triggers for the Boom Bots resolve before all of the summon triggers for Dr. Boom resolves, even though Dr. Boom hits the board first.
This means that whenever you see the card text "after you summon", those triggers will hit the Boom Bots first (e.g Sword of Justice). The card text "whenever you summon" will trigger from Dr. Boom first. Effects that care about the order in which minions are summoned (Vanish, Duplicate after a board clear, etc) will trigger on Dr. Boom first.