Can we synthesize alcohols by the photolysis of hydrogen peroxide?
I do not believe so.

The mechanism of decomposition of $\ce{H2O2}$ is:

$\ce{H2O2(g) -&gt; 2HO.(g)}$

$\ce{H2O2(g) + .OH(g) -&gt; H2O(g) + HOO.(g)}$

$\ce{HOO.(g) + .OH(g) -&gt; H2O(g) + O2(g)}$

$\ce{.OH(g), HOO.(g)}$ are both radical compounds. 

If you take a look at the first step in the mechanism, it is the rate limiting step and it is the same as your first step in the mechanism, the photolysis step.  Therefore if $\ce{H2O2}$ undergoes partial photolysis all that will happen is that the sample will undergo decomposition quicker.  

Additionally, your mechanism of oxidation has been proposed before.  You can take a look at this article, in the section Mechanism of Oxidation by Peroxides: Radical or not Radical, That is the Question, in the end of subsection 4.1 and 4.2 they refer to the mechanism you proposed.  They end up proving that it proceeds through a concerted mechanism that requires the presence of a suitable metal catalyst.  It involves oxidative insertion or some type of $\ce{C-H}$ insertion by the metal followed by oxidation of the product of that reaction.  

But say the generation of hydroxyl radicals does work out, the corresponding alcohol may not be the only product that forms.  Hydroperoxides have a tendency of forming as well.  This is because hydrogen peroxide tends to decompose into oxygen and water, the oxygen can interact with the alkyl radical to form hydroperoxides.  Along with the fact that the alcohol formed will tend to undergo oxidation in the presence of hydrogen peroxide and hydroxyl radicals.

Also if you are still going to try the reaction, the bond dissociation energy of the $\ce{O-O}$ single bond is around 146 kJ per mole. So the energy per molecule is $\ce{2.433\times10^{-19} J}$.  So the maximum wavelength of light to ionize this is $\ce{8.21\times10^{-7} m}$.  Your calculation is a little off, it is in the near infrared range (you may have forgot to convert from kilojoules to joules or something like that).  This is why hydrogen peroxide is stored in dark bottles and told to not be put in the presence of light.