Generally, no. Because there is a bridge that you can use at any time, the value of the tokens remain relatively the same. For example, if you purchase Floki Inu on the Ethereum blockchain, and then when you are ready to sell you see that the price of Floki Inu is slightly higher on the Binance Smart Chain, you can always bridge your tokens to the Binance Smart Chain and sell for the higher price. There is no fee to bridge.