Even at the best of circumstances seeing the aurora is not guarantied. Rumor has it that you have a 50% chance on the best of days.
You are not having the best of days, with a prediction of only 2 out of 9, relatively short nights and longish twilight periods.
If there are clear skies, you have a chance to see a little, but even just enough to be able to say that you have seen the northern light is fun.
If the sky is not going to be clear at all, forget it. You need clear sky on all levels between you and the north.
As you are in the right area and the nights start early enough that you can go out and still have some night left, it is worth a try if you do not have to spend a lot of money.
On the other hand, if you only can go out if you book an expensive tour, you better talk with the locals and ask their advice.
I am not an expert, I have been in Reykjavic in September and have done two nights where I have been 'hunting' for the northern light. The night where I was with a big tour we did not see enough to catch it with our own eyes.
You are (often at least) offered a ticket to come again on an other night, but I did not have the time to make use of that. The other night I went out hunting I had been to a horse show and on the way back the driver/guide stopped and we had a look.
There was not much but just enough to say I had seen the lights.
If you have the right kind of camera you will want to know how to set it to long exposure and have all you need to aim it and leave it with its lens open. My camera was not suitable.