Yes, heating will be fine. If you look on the 3 way valve, there should be a small lever or thumbwheel. Moving this into the 'Manual' position should wedge the valve open to allow the hot water from the boiler both ways to heating and cylinder. Should get you some hot water but will override the thermostats so boiler will keep going and water may get extremely hot!
The 'ice cream shaped' valve you describe may be an automatic bypass valve, any chance of a picture of valve etc to be able to advise further? Opening it wont bleed anything, bypass valves are to allow a flow through the system when boiler shuts down to disperse residual heat.