Whitfield Profile 20 Air Intake

I have a Whitfield (Lennox) Profile 20 pellet stove. When I bought this house 4 years ago, it was already there.
The air inlet on the back of the stove is not piped anywhere. It uses the air from the finished basement.
It has been working fine for the most part these past 4 years but I just had a new propane forced air furnace installed and it uses a cold air intake.

So that had me wondering.....
Should my pellet stove have a cold air intake?
What are the problems or disadvantages/advantages in not having a cold air intake?
Are there any safety issues with NOT having a cold air intake?

Thanks...

The idea is that you will not be using air you've paid to heat for combustion. Look at the tube inside the stove though and you'll see it has a couple holes in it. To me that would leak more cold air into a room than the stove takes out while burning. Another advantage could be that house pressure could be considered a non-issue, but with forced air combustion that's almost no real benefit either.