You can always invest anytime on those casinos. Most casinos have a minimum of 0.01btc for investing on their bankroll
I dont really think that 0.01 btc is something that is worth to invest. Sometimes there are thousand btc in one site so 0.01 is not really worth it. You could have better chance of getting profit if you just gamble that instead of throwing it away into investment, you wont get any profit because It is like less than 0.1 % of the bankroll