No, this colony wouldn't move in.
At swarming time you could have luck that your box might attract them,
...most likely not on new equipment, and the box bait would have to
be far away from the colony...at least 50 yards placed high up.
Your only fair chance you have getting a hive from this colony is....look
for swarms everyday when the time comes and collect them.
They mostly settle on trees not far from hive but you have to get them
down the first day.
I collected two this year from my two colony. I love swarms!

Konrad

Thanks for your help...I will watch for swarming time and try to collect them then. Is there a specific time for swarming?

Usually at, or just before the peak of the season here and last for several weeks, not sure where you are?

Okay...thanks...Also, I have another question, the equipment that I have is used and there is a slight scent of honey. So I was wondering if that would help attract the bees during swarming season?

I am not sure if this would be relevant to you, by increasing your knowledge you have answer to lots of questions surrounding beehive. A good book to read is Beekeeping for beginners that can be find in here at www.bees-keeping.com

Here is a link that might be useful: bees-keeping.com

It would help...also put a couple of drops of Lemon Oil..Google swarm
lures.

Okay...Thanks for all of the help. I will check into that book and Google swarm lures. I will also look into getting some Lemon Oil. Thanks again...hopefully I will have some bees in the near future... :)