Do you already know where you're staying in Florence during that week?
Just asking to see whether you really will be using the bus for that entire week - and you have to use it at least 3 times per day to really say it was worth getting the pass, instead of getting another form of ticket. I personally buy the Agile 10 euro card which is worth 10 rides of 90 minutes each - making each ride cost 1 euro instead of the usual 1,20 euro.
Or I buy the 4x90 ticket which is for 4 rides at 4,70 euro, it costs a bit more than the Agile but if you're not sure you'll be riding the bus 10 times, it makes more sense than going ahead and spending 18 euros for the 7 day pass.
We will be arriving at Florence airport so I will get the shuttle to SMN and get bus tickets. We have rented an apartment near Piazza Guglielmo Oberdan, so we probable use the bus to get around and I thought it would be easier to use a 7 day pass. Do you have to validate the 7 day pass each time you get on a bus?
Then, yes, the pass will be useful: you can pick up bus 6 right on Piazza Oberdan and it will take you to Piazza San Marco before heading to the train station. From San Marco, you can walk to Piazza Duomo in 5 minutes if you don't stop to do window shopping or for anything else ;-). All of the sights are close by.
Do you think you'll be coming back to the apartment during the day, then going back downtown? Because you could still buy the Carta Agile for 10 bus rides at 10 euro for each and use as needed. If you run out, buy the 4 multiple one (more common and sold at bar/tabacco shops and which you can share) for any more you think you'll need. Just trying to be useful ;-)
And no, the pass only needs to be validated the first time you get on the bus, as the 7 days start right then. The same applies for all other passes.