It depends on the antibodies you are using. I don't have experience of probing for IR specifically, but have used immunoprecipitation to improve the detection of other phosphorylated signalling proteins. It is especially useful when the phospho-specific antibody is not particularly specific. Having the receptor IP'ed first helps cut down on background. 

Which antibodies are you using? Perhaps someone here has used these ones. I would try without IP first anyway, since doing an IP, as well being extra time etc, may also increase the risk of losing the phosphorylation before getting to the blot. I find with signalling molecules, the quicker you can get them from the cell to the western blot membrane, the better for results.

Agree with Amanda- try a regular western first (make sure your lysis buffer has phosphatase inhibitors as well as protease inhibitors!) before you go the IP route.

Agree with Alyson. IP is not necessary for detecting those components involved in INS signaling. It is a good idea to try regular WB first. To minimize the strong background you may want to try IP. 

BTW, for phosphor- proteins you may want to use BSA for blocking. However, BSA is not always better than regular blocking buffer such as non-fat milk. It mainly depends on your antibody. A pilot study maybe useful to optimize outcomes. 

I am currently using the Insulin receptor pTyr 1150/1151 rabbit monoclonal antibody from Cell Signalling (#3024) and this works well in direct Western blotting. It needs enhanced chemiluminescent substrate to detect the signal in rat adipocytes but the bands are clean and shows well the insulin activation. For the total insulin receptor beta subunit I use the Sante Cruz antibody sc-711.

In our experience, regular WB works ok, except in case there is no commercial antibody available. Then, it could be convenient to try immunoprecipitation.