Yes. Here is part of an article discussing shorting stocks:
If the stock goes down after the sale of the 1,000 shares at $50—say to $45—then $5,000 is moved from the broker's account to the short seller's account, which can be removed by the short seller. His margin requirement goes down by 50% of the $5,000. On the other hand, if the stock goes up to $55, then $5,000 is moved from the short seller's margin account to the broker's account and the short seller's minimum maintenance requirement will increase.
These money transfers take place exactly the same way whether you do a regular short sale or a naked short sale. There are similar future transfers if you have sold calls or sold single stock futures. When you buy puts and fully pay for them, there are none of these money transfers after the purchase, although the value of your account certainly fluctuates as the value of the puts fluctuates.
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