If listing will start before close the ICO the price on the exchanges may be less then the price of the token sale. That is why projets start listing only after the end of the token sale.
I know only one example of the opportunity to buy tokens on the exchange before the end of ICO. But the trick was that you could buy tokens; sell opportunity was not

.
I have seen 3 such ICOs. In one even took part. When I bought tokens at the same price, and after 2 weeks, when the sale was already open, the price of the token became less than the purchase price, and only after a month went up. I barely returned the investment.
I here for the first time about such situation. Sometimes ICO projects sells there tokes through the exchange but for the nominal price. But after the end of the token sale tokes are listed at this exchange at market price.