If unexpectedly in IMC, does it help to climb into clouds to get on radar?
Absolutely not! If a pilot is not trained for instrument flight it would be near suicide to attempt flight in cloud due to spatial disorientation. In clouds you have to trust your instruments solely and be able to interpret them, which requires special training, retraining and practice. Without these pilots do not last long in cloud, see this related question for lots more details on inadvertent flight into IMC, which is applicable to your question. 

What the pilot should have done is made a precautionary landing on one of his concrete compass lines or a field while he still had the option to do so. Instead, he had get-there-itis and got himself perished as a result.