Unless your game system does something with numerically expressed experience points, the actual value of points is irrelevant.
No, there would be no effect of zeroing XP each level in D&D 4e using the standard (as printed) XP values for levels and encounters, other than levels taking a progressively longer time to attain (the MMORPG "grind" style of decelerating progression).
D&D 4th edition has a few entirely arbitrary number systems, and XP is one of them. The values as presented in the books aren't inherently meaningful; you could change those values and change all the values of XP that monsters and quests give and come up with entirely different values and the game wouldn't really change, in and of itself. All that would change is how quickly your players go up levels, and that's already something DMs have a huge amount of control over. Consider, for example, that some DMs simply forgo XP entirely and declare their players level up at story-appropriate moments.
As others have pointed out, the XP system as written is balanced with monsters, which have XP costs, and encounters, which have XP budgets, all in the intention of having about 8-10 encounters per level. You could abandon XP and just track encounters and level up characters after every 8-10 encounters.
But XP was meant to add some extra nuance or reward for characters that find creative ways to bypass encounters. If you don't want players to feel penalized for negotiating with orcs rather than slaying them, you might give the same amount of XP for the skill challenge as you would for the battle. The point of experience points, really, is so that, each time you deliver them to players, players know they did what they were meant to do.
In reality, it's just a pretty raw and basic reward point system, a pat on the head, a Pavlovian bell, as it were, to get the players salivating.
Zeroing them for each level might have some psychological effect beyond having to change the math on how much you need per level. Note that many MMORPGs zero XP each level. Also note that many MMORPGs are designed to slow down leveling as players progress. However, the psychology of zeroing is meant to make it easier for players to know how far, percentage wise, they are in leveling up: 1,247,285 of 2,500,000 is a lot more clearly 50% than 1,247,285 of 1,300,000 (when the last level was at 1,200,000, but you don't see that information anywhere).
Arguably, a simpler XP system than the one in D&D 4e would be to zero after each level and level up at a fixed value, such as 1000 XP. Then players always know exactly how far into the current level they are. Each encounter would deliver about 100 XP, give or take a few points, based on the DM's discretion on difficulty and such.
As for the effects of the raw change to D&D 4e play if you zero XP each level and make no other change, it slows level progression by about 5 times. As wax eagle points out, it creates a parabolic XP curve which rapidly slows from levels 1 to 10, going from 10 encounters up to nearly 50, and then hovers around 50 encounters per level from levels 11 through 30.
Of course, maybe you want a slow campaign with about 5 times more content per level. At which point: go for it!