Absolutely the iPhone had an influence. Likewise, the iPhone design was not created in a vacuum. It was a result of decades of industry advancements.
While Apple sat on the sidelines for two decades, phone makers had evolved multiple form factors, from clamshell to the basic touchscreen display slab that Apple used. The industry had figured out the best place to put internal antennas, which Apple used as well. The industry had figured out that physical power, volume and home/menu controls were a good idea even with a touchscreen device.
Far more importantly, all the major software elements of a smartphone had been hammered out long before the iPhone implemented them: phone functions, texting, user apps, settings page, camera, video player, web browser, location services, and others like video recording and MMS that took longer for Apple to include.
In other words, the hugely critical, and design time consuming, starting point was already plainly laid out for Apple due to the work of others. They had only to copy and refine from there. And in fact, they added very little new base functionality: offhand, visual voice mail is all that I can think of.
As for the touch UI, don't get me started on how obvious the base design elements were to those of us in the field. The fact that phone makers had not implemented such in mass consumer devices, does not change that. There were no big surprises in the first iPhone demo in this area.
So, considering the entire iPhone, one could argue that Apple was influenced as much or more by the previous smartphone R&D of others, than the relatively surface enhancements that Apple themselves contributed to the smartphone definition.