Dissolve them? I presume you mean degrade them? They are usually already dissolved before dosing.
If the question arises because someone told you that you need to dose more iodine because of the UV light, then I would disagree. I do not recommend that most aquarists ever add supplemental iodine as its benefit for any organisms that we keep is undemonstrated. The transformations of different forms of iodine is probably largely biological in aquaria (it is in the ocean) and not primarily driven by lighting unless you use a UV sterilizer. There is, however, the potential for lighting to have some effects on the iodine speciation in aquaria. UV light drives conversion of iodide to iodate. However, iodate is the primary species present in the ocean, so it is not unnatural, and is bioavailable to some algae and bacteria (although perhaps not as readily as iodide).
If the iodine supplement is Kent's time released compound (presumably an organoiodine compund), I do not know what impact the lights have on it, but I do not recommend using it anyway.
That said, there are many reactions that are driven by light in aquaria.
Many organic molecules absorb UV light, and can then more readily be oxidized. The same is also true for certain inorganic compounds,
including hydrogen sulfide.
So to be photodegraded, molecules first need to absorb the light, and then be prone to a breakdown reaction from the excited state that the UV absorption has put them into.
However, I would not conclude that such reactions are necessarily bad. Iron EDTA complexes are made bioavailable for organisms to use primarily after being photodegraded in an aquarium.
Discussion of photo reactions are scattered through my different articles. These articles have more:
Iodine in Marine Aquaria: Part I
http://www.advancedaquarist.com/issues/mar2003/chem.htm
Iodine in Reef Tanks 2: Effects on Macroalgae Growth
http://www.advancedaquarist.com/issues/april2003/chem.htm
Organic Compounds in the Reef Aquarium
http://reefkeeping.com/issues/2004-10/rhf/index.htm
Hydrogen Sulfide and the Reef Aquarium
http://reefkeeping.com/issues/2005-12/rhf/index.php
First Iron Article: Macroalgae and Dosing Recommendations
http://www.advancedaquarist.com/issues/aug2002/chem.htm
Second Iron Article: Iron: A Look at Organisms Other than Macroalgae
http://www.advancedaquarist.com/issues/oct2002/chem.htm