Yes its possible (in theory).
However, it can also cost more.
I speak from the experience of being a (former) lender (and son of a builder).
Do you know the right tradespeople?
Do you know in which order they need to work?
What would you do if the electrician you booked didnt turn up and the plasterers were due to arrive soon?
Even weather caused delays can cost you in dollars.
Can you afford the time off work? i.e. will the money you lose not working cost more than the possible savings?
Do you have building industry experience? If not, forget it!
If the work is financed, most banks wont release payments until certain stages of completion.
Do you have the money to fund the work until the bank pays you back?
Youre better off with a contract.