All I can really give is my personal experience. I'm late deafened and have absolutely NO hearing left what so ever. I've only been Deaf a few years (I say Deaf and no deaf because I grew up in the Deaf Community and everyone thought of me as Deaf even before I became physically deaf. Make sense? I just don't want to offend anyone.) and I apparently still talk fairly normal. I have to really concentrate on annunciating, pronouncing, and remembering words. If I'm tired or just not really paying attention, apparently I start to slur my words a bit and basically start speaking in ASL gloss. I also for some reason do aquire a full Deaf accent if I'm signing and speaking at the same time. I believe this is just because I'm concentrating on my signing and not so much my speech. I know one thing I tend to do a lot if forgetting words. I'm usually able to know the sign for what I'm trying to say but I just can't think of the English word. I can't remember how to say it, pronounce it, or sometimes even spell it.
I think for the most part if you just continue to use your speech, you shouldn't get much of an accent. You may just start to slur some words here and there. I personally have slowly started to become voice-off this past year. I do still talk to close friends, in emergency situations, or if a conversation will only consist of a few words, such as getting checked out at the grocery store. I do lip read extremely well so it's been a bit of a problem for me because people tend to assume if you can speak, you can hear. With some people no matter how many times you say, "I'm Deaf, I need to read your lips." they just CAN'T get it through their head. So I've just made a personal choice to use a pen and paper when I'm out in pubilc. It's helped me a lot because not only do I have issues when people don't understand I'm Deaf but I also just feel very uncomfortable using my voice. However, I have made sure not to completely stop speaking. Like I said, I still talk with my close friends quite a bit. I do think if I stopped speaking at all my ability to speak as clearly as I do would dissipate pretty fast.
So after all that, I guess to answer your question, I do believe you can aquire a Deaf accent as a late deafened person. I'm pretty much in the early stages of it and I've only been Deaf a few years.