I am a committee member of a non-profit organization that
provides information-technology related service to under-previleged
communities. We are encountering some concerns from our board members
that we might be competing with private sectors. We would like to know
any studies on whether / how volunteering from non-profit organization
competes / threats / helps private industry.

Last I checked, bread lines and soup kitchens weren't putting
restaurants out of business.  I suspect this will be a difficult
question to answer because so much will depend on the particular
business environment you're talking about, but in general, it's easy
to imagine hypothetical markets where volunteer labor and services
provided for poor "clients" doesn't significantly harm or disrupt
for-profit businesses providing related services.

x = how much business you are taking away from one sector.
y = how much business you are giving to another sector for the
consumers have more money left after not needing to pay for what you
guys gave them.

x = y and thus the effect is nill.

But off course, those guys with concern are facing the effects of x 
but reap no benefits of the increase in y.
So you will be opposed by certain selfish individuals, even though
society gets better for your actions.

Almost any type of aid to those who cannot afford to pay the going
price will be misused by someone who could pay.
If your organization tries to assure that its support is going only to
those who cannot, it would not be competing with private industry.

Thanks everybody for commenting. Seems it's more complicated than I
first thought and deserve more research.