Yes and no. Can you get in great shape at home? Yes of course you can lift run ect... all at home.
So why go to all the work of finding a qualified instructor? You need partners, you need a instructor. A home! Someone that has been there, done that. Someone that will help you get as good as you can be as fast as you can.
When I was in South Dakota I was essentially training by myself. I had bought VHS tapes and would watch them and practice the moves on my friends. I did this for a couple of years while I was in college and got to almost the blue belt level by doing this. But if I had been training with a real coach. I would have been a lot farther along than what I was by doing this. Also I would have never achieved the level or even remotely close to it by training by myself in South Dakota. Keep in mind I was lifting, I was running and I was in great shape. But I lacked the partners I needed in order to improve. I also lacked a coach or teacher.
I knew this at the time and that is why I moved to Texas all the way from South Dakota to train. I did this as soon as possible. Because I felt like I was falling farther behind in comparison to the guys that I had met on my trips to Texas. On a side note, it is crazy the amount of guys I am still friends with. Guys that I met on those trips from South Dakota to Texas 20 years ago. Guys like Kenny (Black Belt), Buddy (Black Belt), Orlando (Black Belt), Robert (Black Belt), Tim (Black Belt). And there are others that I met almost 20 years ago thru Jiu-Jitsu that I am still friends with to this day. Plus my friend Paul that moved with me from South Dakota to Texas. He didn't move for Jiu-Jitsu. But fast forward 21 years and he owns a Jiu-Jitsu Gym and teaches other people how to run there own Martial Arts gyms. He couldn't being doing either one of those things if he had stayed in South Dakota.
Should you do all your training at the gym? No absolutely not, I am a big believer in Mental training. And practicing things on your own. I am talking about shadow boxing, running on your own, and mental training. All things that you should be doing on your own. Shadow Boxing, your boxing coach should have you doing this in practice. But you should also spend 30 plus minutes a week on your own.
You should be doing your base training. Heart Rate training at least 3 sessions of 45 minutes, one hour, and 1.5 hour a week sessions. Keeping your Heart Rate at 70% of your max or 220 minus your age, times 70% will tell you your average you should be shooting for. Mine would be 220-43=180X.70= 123. So I would keep my heart rate between 120 to 130 beats a minute for one session of 45 minutes. One session of 1 hour and a 1.5 hour session keeping my heart rate between 121-130 beats a minute. If you do this you will get in amazing shape where the rest of your training will seem easy. I started doing this for my last 2 fights of my career. It really did make a huge difference. Think of it like, training your heart. So your heart is in shape so when you need to explode you can.
Mental training: There are lots of different thoughts on mental training. But I am a huge fan of mental rehearsal. What I am talking about is basically spending 10-20 minutes before you go to sleep. Running a match or a fight or whatever your sport is thru your head. Imagining everything possible down to the second. Go thru how you would come from behind to win. Or you are up on points and are caught in a arm-bar, how are you going to survive and escape the position ect.. Your body can only train so much but your brain can handle far more training. So use it to it's full potential. This is just a couple of ideas on training that you can do outside the gym. But they are in no ways a replacement for the gym training. Or having a qualified instructor to help you to reach the next level.
Conclusion: If you live in a place where you don't have a good gym or qualified instructor to train with. Do your best training with your friends ect.. But if you live in a place with a legitimate gym and a good instructor. Even if you can't afford the gym join the gym, pick up a second job to help pay for the training it will be worth it. Most places are going to charge you under $100-200 a month for a World Class instruction. This type of training will make you in to the best possible fighter that you can be.
This is a small price to pay to train with someone who has been down the road that you are wanting to go down. So suck it up and make the commitment to your training. Train at home and go to a real gym and train with the best possible training that are available in your area. If you don't have a good gym and do what I did and move 1000 miles to find good training. It was the best thing I ever did for myself moving to Texas. I love South Dakota but Jiu-Jitsu my real passion. It wasn't available at the level I wanted to train at there so I had to move. It also opened a door into what I ended up doing for a living Teaching Jiu-Jitsu and MMA. My whole life now centers around my gym, my friends and family and they all started from Jiu-Jitsu. So what are you waiting for? Find the best gym you can and start training now and change your life forever!