Networking does help a lot. For me, it just opens doors to oppurtunities. Let me explain. At my last corporate job, when someone left the department relied on the pilots contacts for interviews, long before it was advertised on the net. It eventually still was advertised, however our buddies got phone calls first. That was just to "test the waters" of interest, and eventually lead to an interview, with the people they got applying from online sources.
But many, many corporate jobs are still advertised, and do require a certain ammount of good flight expeirence. Mainly jet time/pic turbine, multi engine, and unfortunalty time on type in a lot of cases. But time on type mostly isnt a pure deal breaker as most departments still do the 6 month recurrent training. So youd be going to FSI or simcomm either way.
But let me make one thing perfectly clear. If you dont "fit" with the culture, they will not hire you. They want pilots who not only can be good pilots and PIC's, but also good people to spend time with at, and outside of work duties. Any respectable corporate department, large or small, treats pilots like a employee of the company. So they want you to stick around, not just bail in 12 months. And they also may expect some above and beyond duties, in comparison to a 121 job. Similar to good customer service from a charter flight. For example, On long day trips, I would ask my few passengers if they needed food or drinks on the return flight. Since I go into town and buy my lunch anyway, it wasnt hard to go a little further and get them food if needed. Hardly ever had to, but just the offer was one of those "above and beyond" things they loved. Especially since they took a chance on me with very low total time, and no time in type actually. Keeping the hangar clean, cleaning the plane in between flights etc may sometimes be needed. Obviously if its a large jet, chances are you wont be washing it yourself. But a smaller King Air or PC-12 they might want it looking presentable. Especiialy if you fly there clients too. some places like "jack links beef jerky" (search it on APC) wants people cleaning bosses cars during free time,and doing janitorial office work, and serving drinks on an aircraft that requires two pilots. Thats over the top for sure, but to some extent, things like that are somewhat expected. Just not to that extreme. Its like flying charter for the same people, every day. A clean plane, basic needs for passengers should be met and still with a smile! Haha