Unfortunately not, at least not by the method you propose.
According to the original patent,
Patent US2176181
, the Hunsdiecker reaction only works for the production of alkyl chlorides and bromides. With the iodides the conversion stops at the ester; this is called the Simonini reaction. To quote the patent:
In the German periodical Monatshefte fuer Chemie, vol. 14, page 88 et seq. Simonini describes a process in which iodine, reacting with the silver salts of fatty acids yields a product which upon heating, changes into CO2.AgI, and an ester R.COO.R in which R represents the hydrocarbon group of the fatty acid.
One might expect a similar reaction if chlorine and bromine were substituted for the iodine.
As appears, however, from the method forming the subject-matter of the present invention, the reaction of the silver salts with chlorine or bromine proceeds completely differently; viz. according to the following equation:
R.COO.Ag + Br2 = R.Br+CO2 + AgBr
There are, thus, obtained from fatty acid silver salts and chlorine or bromine, and with the splitting-off of a C-atom besides AgCl, or AgBr respectively, the alkyl-halides. The reaction is not restricted to the silver salts; it proceeds in the same manner also with numerous other metal salts, especially with those of the first, the second, and the third group of the periodic table of the elements.
See the following Merck Index Name Reactions for further explanation and some literature references:
Hunsdiecker Reaction (Borodine Reaction)
(
http://themerckindex.chemfinder.com/TheMerckIndex/NameReactions/ONR200.htm)
Simonini Reaction
(
http://themerckindex.chemfinder.com/TheMerckIndex/NameReactions/onr368.htm)
That said, acetic acid
can be used to make methyl iodide. It has been reported, in
Chem. Ber. 42 (1909) 3868, that the potassium salt of acetic acid in the presence of either iodine or potassium iodide can be transformed into methyl iodide via electrolysis.
I don't have the article handy so I can't give any more details or comment on its feasibility. However, I'll have a look at it next time I'm in the library: it sounds an interesting proposal.