No, it's not. Investing that money would be about the long term horizon. Like, 10-30 years at least. If you're trying to get ahead, your current goals should be getting and staying out of debt, and preparing for emergencies. What happens if you throw that emergency fund in the market, there's a crash, and then you lose your job in six months?

Get out of debt. Build an emergency fund. Start investing. Then re-think your emergency fund strategy if you really want.