2000 mercury grand marquis

I had a shop check my car out and they came to the conclusion it was my PCM so I priced it at ford they wanted 1200 for part and labor so I just went the cheaper route and got it from auto zone I gave my exact mileage and vin # I was told by the person that helped me I could just plug the new 1 in and it will crank and run so I tried it and car backfired so I called ford and come to find out I had to get the PCM programmed so I did and car cranked but shut off so they ran more test and found that due to the backfire it blew a hole in the intake manifold they want 1800 to fix but I’d rather bring it home and get my mechanic to change it for 150 and get the part from auto zone for 260 my question is could the problem with the intake manifold cause the car to start and then cut off?