I believe a coach is most important when someone is young and learning the game. They can be shown and taught the 'right' way. After that it's a matter of a coach using his skill to assess every player and make improvements while not destroying them. We are not pro's so can't do the hours it takes to make major flaw changes.
I still mainly think though it's down to the individual, if they really want to improve they will. Plus confidence.. As it seems with all aspects in cricket.. If you believe you can bat, if you believe that mr angry bowler actually isn't going to get you and your confident in yourself you will do well. May not play for England but you'll do well.
I've had no coaching (barring the odd comment but nothing proper) and didn't play when I was young so I've only really been learning now for 2 seasons and this is my second winter and I'm improving. Yeah I won't look like the most technically gifted player but so what.. It's not about what you 'look' like (although people do judge on appearances!!), its about runs.. Do you score runs??? Yes or No. I don't play ECB Prem but just under it so it's a respectable standard, and that's without coaching or having played long. Just train hard and work out what your good at, what your bad at, work out ways to eliminate the shots that get you out and play the percentages.. It's surprising how much just that will help, at any level.