Not necessarily. Remember for every seller there must be a buyer. It all depends on what the buyer wants to pay and what the seller wants to sell at. It also depends on if these new shares are from a split or new equity.
If this is a 2:1 split then yes the listing company will half the price immediately. You won't lose value; however, since you doubled your shares.
If this is new equity, then the price may not reach half. Usually if you double the shares, you half the EPS and double the PE ratio. This means sellers are likely to want to get rid of their shares since earnings have been halfed and the current price looks way overvalued. Buyers won't buy unless the stock reaches a level of EPS that they are comfortable with. Most likely they won't buy until it reaches $5/share but the market may keep it higher because the company is in demand and people wanted shares to begin with, there just weren't enough to go around.