Demo account trading is definitely important before live trading especially if you are a newbie and if you are planning to trade manually in order to get yourself familiarise with different options available in MT4 which you can check and practise in real time with no real money loss.
But if you are planning to practise in demo for few days and jump into live account after that, then it might not be a good idea. Until and unless you have thoroughly tested and practised your specific strategy for long periods of time in demo and generated consistent profits, till then you should stay away from live account and continue with demo account only and it will save you a lot of money.
If you are successful in demo account with your strategy with an average of good pip expectancy and low drawdown % with a track record of 3 to 6 months , then in fact you don't need live account of your own and you can easily get investors or get connected with partner brokers whose money you can trade and make money without any investment of your own.
So being consistently profitable in a demo account with good and long track record can also help a lot without any investment from the trader.
In fact, live account trading is not necessary if you can meet the following 5 conditions in your trading:
1.Good pip expectancy of 5 to 10 pips per trade or more
2.At least 100 trades per month
3.Low drawdown of around 10%
4.Minimum monthly return of 5% to 10% per month
5.Minimum track record of 6 months or more.
If you meet all the above 5 criteria, then you don't need to trade live account. Instead, you can simply continue to trade in that demo account and if needed then connect your demo account to a live account through a trade copier software and still you can make profit through trade copying to live account.
At least you can provide trading signals through signalstart and make money or join a PAMM account of broker and there are many more options.
So it doesn't matter whether it is a demo account or live account, but all the above 5 points must be satisfied since each and every point is important and has a reason behind it which describes clearly that there is a 80% to 90% chance that you are already a successful and professional forex trader irrespective of demo or live trading.