Is the Xbox brand insignificant at #2 to the point that it's going to have a snowball effect and 3rd party developers will pull away? The OG Xbox had that problem. Nintendo had that problem when they were still competing directly with Sony.
No it wont cause 3rd party publishers to pull away. What is will do is make it harder for MS to secure exclusives from 3rd party publishers because the allure of the PS4 is too strong.