Coming out first absolutely affects it, but it's obviously not a surefire guarantee.
In each generation where the victor was the earlier one to release, they developed a significant foothold before the competition even released.
NES vs SEGA Master System.
GameBoy vs Game Gear.
Playstation vs N64 and Saturn.
PS2 vs GCN and Xbox (minus DC, which died off for separate reasons)
DS vs PSP.
In each of these cases, the earlier system to release was the system to win. It had already built itself a strong lead over the competition prior to the competition's release, with developers already setting strong plans for them and the system already developing a strong reputation amongst consumers.
But that obviously can't be the only thing. There have to be other factors to include as well, and ones that are much stronger than JUST "releasing first".
NES had the fact that it was vastly superior to anything previously released. It had graphics that could be recognized as actual shapes, not the stupid "block people" that you got on Atari games and the lot. It offered the experience of the arcade... at home!
GameBoy did similar things to the NES - provided never-before-seen handheld gaming. Before the GameBoy, you had Tiger or Game-and-Watch experiences on handhelds. Trash. GameBoy offered gaming on a level similar to home consoles... and with a brand-name that had taken the world by storm!
Playstation was a freaking CD player that also played THREE DIMENSIONAL videogames. HUGE concept in the early/mid 1990s.
Playstation 2 offered vastly upgraded graphics, was a DVD player (which was a huge thing in 2000), AND had the immense reputation of the Playstation to ride on. This is probably the weakest example on this list, but it also had kinda lousy competition, so it didn't NEED a very strong argument.
Then the DS vs PSP. DS was riding with the reputation of the Nintendo handheld brand, Nintendo's IPs, and now true 3D handheld graphics. It MADE handheld gaming a serious concept again, no longer just the "kid's time waster". PSP helped do the exact same thing, but it didn't have the handheld branding, it didn't have the IPs, and it didn't have the touchscreen. It was also bulkier.
None of the recent first releases (3DS, WiiU) have the same special tricks to take their leads. 3DS has the 3D gimmick, which is nice but won't take it that far. WiiU has the touchscreen, but that's nothing new to gaming so it won't make a huge difference. They BOTH need more than just their special gimmicks and releasing first to guarantee their lead this time. This generation, it's just not quite enough.