My opinion, and my opinion only- YES!
On the student experience, a well-run school with adequate resources makes your efficient training less than an accident.
Flight training is an intensely personal experience. You and the instructor have to "fit". An experienced and resourceful teacher can usually find a way to adapt to different students, but the possibility of failure exists. A school with many instructors help against that.
The way you train will be with you forever in one fashion or another. Your initial professional experience is very much a reflection of training, but you'll learn and adapt. My opinion, and perhaps controversial is that immediate response emergencies and your success in dealing with them will be forever influenced by your initial training. When the stress is on, the first and strongest response will be very much shaped by your first training.
I'm amused by those who pick their school primarily by cost. Not diminishing the importance of a realistic budget, but won't necessarily select the cheapest physician, surgeon, dentist, accountant or legal, representation because quality of service is a very important criterion in life-changing situations. The way you fly very definitely impacts your life...