Definitely, but it depends what it is.
Powerful system will get initial support from most Devs (EA/Ubi/Activision/Square Enix)if Nintendo is also pushing a strong line up which looks like it will grab a core gaming audience, Zelda is a good start. Whether this can be sustained and grow would be dependant on whether the games sell, NX third party games will need to be superior to PS4 in terms of performance and released on time. Nintendo personsl reward system could help with this aswell, free online is a bonus too. Online centric games with a legacy audience on other platforms will be weak sellers and there's no getting around this unless Nintendo manages cross platform play with PS4/PSN. New ones like Overwatch will fair better imo.
A unified platform is the safest way to get support because the handheld aspect of the system will push the user base fairly high, fairly quick. Japanese support would be A+, Western support will be strong but the nature of it will be effected the specs. If the home component is weaker than PS4/X1, I think multiplats support will be weaker and the games will sell less. Maybe developers will opt for budget games made exclusively for NX.
If Nintendo is pushing a new controller gimmick heavily, I think you can count most third parties out. If ir succeeds then expect them to be back with cheap exclusives.
Ultimately the NX is going to have to deal with the fact that 80m people are going to have a ps4/X1 come March 2017. Many of its users will likely own one of those 2 platforms so they need to give them a reason to buy 3rd Party games on NX, hell they need to give then a reason to buy NX in the first place.