They don't care who you train with. The training with any school is to the same CAA standards so it should be a much of a muchness. Some may have instructors that instill in you a better sense of professionalism and airmanship but I wouldn't get hung up on this idea you have. It's what you do after you have finished your training that will determine if you get an airline job, and determine the type of pilot you become.
Airlines that you will get your first job with want to see Total Time consisting of mutli pic and multi total, total pic, instrument time. They also want to know you are not a d
head and they could sit next to you all day in an enclosed space.
Instructing will get you plenty of hours and after a few years hopefully some multi instructing. Or try and get into GA and get some multi that way.