The short answer to your question is ..YES. You can root the cutting and if it takes it will grow into a fully mature plant that can give fruit the following 2 or 3 years. The first year it shouldn't be allowed to fruit as it will still be growing its roots and getting established. Also some plants do not do well on their own roots and need to be grafted to something thats more suited to the conditions its being grown in.

Some cuttings root easier and faster than others. If you do a search you will find the easy ones and which ones are nearly impossible to root.
Andi

Some people are successful rooting citrus and some people are not. I am one of the latter. I encountered drying leaves, mites and I spend more trying to take care of them. For a price of $9 to $32 I can have fruit harvested the same year. They are showy and the envy of your friends. HereÂs some sample of my plants before.
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