Is it worth if the entire team takes smite?
Let's assume that we're working from the bottom left corner of the map, so that your bot lane has access to golems, and your jungle path can be blue->wolves->wraiths->dragon.
A lane can probably get two wave clears in, if they're willing to spam abilities and attack whenever possible, not just last-hitting, which is about 530 experience for the solo lanes. You'll probably want top lane to clear the small lizards and wolves so that he'll be less far behind when he returns to lane.
Top will probably need to be running Smite/Teleport, so he can join the dragon on a dropped ward, rather than running the full distance, and tank the dragon after which he can recall, buy, and be about even with his opponent.
The global gold and experience from Dragon will probably really help Mid and Bot lanes, who won't necessarily need to recall immediately, and can use the level boost to be minor lane bullies, although they'll have to be very careful about overextending, because they'll have one fewer summoner than they're used to.
While you will have a lead, you'll be more susceptible than usual to ganks, or less able to convert your advantages into kills. Summoner spells like Cleanse and Exhaust are particularly useful in late-game teamfights, so you need to use the bonus gold and xp to snowball quickly.
While that might look rather rosy, it assumes a certain lack of counterplay. If your team is all taking smite, the chance that you'll be invaded is very high, and even one team member being killed or forced to recall instantly lowers your burst damage by 500 points, probably more than you can recover at such low level.
In summary: I'd consider it a very High-Risk play, and one that doesn't result in more than a moderate advantage if successful.
Every summoner skill has his pros and cons, and Riot Games is trying their best to even out the utility of all of them. All having Smite can be a good thing, even considering you cannot take Flash for example.
When your team is well coordinated, after the laning phase it's possible to dominate the dragon and baron when you are roaming as a team. Usually when a few towers are gone, the two teams start roaming and clearing jungle camps to kill time. After all, when a lane is pushed, you cannot afford to get in too far and get ganked.
In that situation, Smite has both a pro and a con. The advantage of carrying Smite here is that you can quickly kill important monsters (big wolf, big golem, buff minion, etc) and team up to get a 'smite-bomb' on the baron or dragon. The disadvantage of having Smite is that it might go too fast and you'll have nothing to do or pushed too much. But then again, I don't think Flash will be used in this situation more often.
One thing that should not be forgotten about, is the fact you get some gold when using Smite (provided you invested that skillpoint). 'Spamming' your Smite actively gives you a few free wards, for example.
More specific on your question, in the situation at start at the dragon, the plan might fail. For starters when you all carry Smite, the enemy will notice. When everybody is gone, a ward probably will be placed. And two or three hits from the dragon can give you a serious disadvantage in a teamfight on that level. Plus, your toplaner will miss out on a few waves on top. This ofcourse doesn't add up to the fact that your whole team can have quite a bit gold.
So overall, it is not a bad practice to do so. When coordinated well, it can give you extreme advantages in the game. Flash is actively used defensive very often and saves lives very often, while Exhaust and Ignite often enough make sure you get the kill (or get away). Therefore, you'll need to manage to play without that and make sure to not make mistakes. Five people having Smite doesn't weight up against five more deaths.