No. It won't make a significant difference. Most name brand DVD/CD players today have decent digital to analog conversion. You shouldn't need to spend more than $100.
I'd be more worried about the quality of the preamp section in the Pioneer unit you have. When you get the CD player, compare it with everything plugged in through the Pioneer, versus the Asgard plugged directly into the CD player. You may find that Pioneer unit is the weak link. Or it may be OK. But try it.
I did some research and saw some of the $300-500'ish range CD players that were top choices on Headfi. I ended up ordering the Onkyo C-7030 CD Player right around $200. It looks like a decent quality budget CD player and Crutchfield talked about it being audiohile friendly. I found some reviews that were positive for people listening with HPs.
Do most of you who listen to your Grados to an Ipod or other mp3, use portable amps? Or, do you find you listen through an Amp/Dac primarily when listening to dedicate sources. I'm waiting for my Asgard, so I haven't heard the difference yet. I find with my 225i, that I have no trouble powering my Ipod classic and it sounds pretty good to these ears. Maybe when I get the Asgard, it will be like night and day. But, I'm wondering if it is worth the hassle and expense to purchase a portable amp & strap it on while listening to a portable device while moving around the house which is often how I listen to music (with an ipod, prepping dinner, getting ready for work, moving around from place to place). Or perhaps you use portable amps/DACS to take to work to listen to a work computer or a laptop or tablet or something...just curious the context in which folks use portable amps or amp/DAC combos.