Welcome to the forum. You can run the headers w/o a tune but probably wont get any real performance gains. You will need an unlocked PCM and a tuner like Diablo or HP. Talk to one of the vendors here like Modern Muscle. They can set you up with all the parts and a canned tune. If you mean by running open headers that you will not have the exhaust hooked up you probably will have issues. I did that on a 2006 SRT10 I had and it wouldn't idle and smoked like a diesel. Problem was air turbulence from the short run from the O2 sensors caused them to think the engine was running lean so the PCM started pouring the fuel to it.

 

You can run without the tune for a while even with catless mid pipes. You will have a CEL because the O2 sensors after the cats are not gonna like the extra flow. Once you are tuned it will be all good, no more CEL to clear. If I read your post correctly you say you may have to run with open headers for a while. I ran my car with open headers out the subdivision and a quick run on the highway and back. It was beyond obnoxious, everything in and on the car shakes including the insides or your skull. Its fun for about 5 minutes then not so much. Your neighbors will love it for sure. Only thing cool was it sounded like it was a track beast.
Best of luck with your install, I recommend getting the tune done as soon as possible.

 

like stated you can run it without a tune, just not with open headers, Most name brand headers come with mid pipes so no need to run open.
When you are ready for a tune let me know.

 

As you mentioned, without a tune, your engine could run lean, especially at higher RPMs. This is because long tube headers can alter the air/fuel ratio by allowing the engine to expel exhaust gases more efficiently, leading to more air being drawn in. Running lean can cause detonation, which can damage your engine. If possible, try to get the tune done as close to the installation of the headers as possible. This will ensure your engine runs properly and avoids potential damage from running lean. Also, consider the long-term implications of your modifications, particularly regarding emissions and inspections, to avoid legal issues down the road. you can find the best site so you can go to the pros and cons of long tube headers