In order to get full capacity of a beam by adding depth using an attached piece (i.e. gluing and screwing a 2x4 to the bottom of a 2x10) you have to obtain adequate horizontal shear through the glue and screw process. This is certainly possible using the correct glue, and can also be done by using an adequate number of fasteners (screws or nails). The tricky part with glue is ensuring that the bond is solid.
This is basically how glue laminated timbers are made, however they are made in a factory using high pressure and heat activated glue, so the bond is consistent and verifiable. This is not generally possible with home glued options.
If you are going to try it, use the best possible bonding glue, which is typically resorcinol or epoxy, mix carefully, and make sure you get adequate pressure, either by clamps if possible or by immediately screwing or nailing the additional board in place.
I would not recommend counting on the glue and screw method as a primary support, however if the goal is to reduce deflection, and it is not needed for strength, it is a good solution.
Thanks Daniel. Do you happen to know what the wood equivalent is, of adding the 20 gauge/18 gauge/16 gauge straps? Would it be the equivalent of adding x inches in depth? Anyway that I can calculate it?