You can cut and replant (I call it logging), but it's not sending it to your wonder. It's disappearing. Also, you can't rush thru gold, disbanding, or logging an improvement and then change that improvement to a wonder. The game keeps track of whether you rushed it and will not let you switch.
The only way to rush is with a leader.
As for logging, for city improvements it works great. I usually use a stack of two workers. That drops you from 10 turns to 5 turns. I seem to recall adding a third worker only drops you to 3 turns, so you're not getting as much back for adding the third.
Note that it is not free. In a republic or democracy (or in earlier gov'ts if you have a normal size military) you pay 1 gold to support the worker. So you're getting 10 shields in 20 turns (10 to plant and 10 to cut) at 20 gold for one worker, so that's 1/2 a shield for each gold. It's not free, but still cheaper than rush buying (8gold/shield or 4gold/shield depending on your gov't IIRC).
With two workers it is still 1/2 shield/gold (10 shields in 10turns @ 2 gold/turn).
Three workers might give you a slight cost cut if it is really 3 turns to plant and three to cut, but I haven't tested it. (Anyone?
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