Strength of a 2 x 6 when 5.5" long hole is drilled through middle of the 1.5" face?
The purpose of your construction aside, I'd like to address the strength question.
One way to figure it out is by way of an experiment. Load bearing capacity of a joist or beam is based on material strength, direction of fibres and load, point or distributed loads, fatigue and dynamic &amp; static loads etc..
Putting all this together, a L/360 deflection limit emerges in building construction, which states that lumber of length L can be loaded up to the point it deflects no more than L/360. (Caveat emptor: there are variants to this and lots of discussions as to its merits and applicability).
In your case, where published data is lacking, you could perform a simple test: compare two pieces of 2x6, drill your holes and insert screws into one, and apply a defined load on both. Then determine at which load difference both deflect equally.
That relative load difference for a given deflection around the L/360 value is roughly equal to the relative difference in load bearing capacity.
For a 10 foot piece, the maximum deflection from L/360 is 1/3in. You could simply apply a load until the pristine 2x6 deflects perhaps 1/4 or 1/3in, and determine what (lesser) load is required to deflect the perforated 2x6 by the same amount. If the difference is within say 10% you have little to worry about.
Note that bores with screws inserted will have a different effect from empty bores: the screws restore some of the lost strength in the upper compressed portion of the lumber.
To apply the load you can rest the ends of the 2x6 on stools or chairs, sit on the centre (with a friend), and hang a bucket off the centre which you fill with water, steel weights, rocks etc.. for fine tuning. It may take 300 to 400lbs to reach 1/4in deflection (It's a guess, I haven't tried it). Longer lumber will get you there with less weight but also provide the relative difference you seek. Make sure you prevent the lumber from tipping.