Hot water heater T&P discharge going into furnace condensate pump?
If the T&amp;P relief valve opens for most reason it is designed for, (over pressure or over temperature) the  water flow can be a slow trickle or could be a fast and sometimes violent event. If it is a slow trickle, the pump will handle the water but if it a quick discharge there is going to be a lot of water flow. As far as the valve on the hot water side of the heater, I have no idea how that will alleviate any of your problems, unless i do not understand it's function. Without a drain in the basement, I would not store anything in that area that could be harmed by water. If the water heater's T&amp;P valve is flowing a small amount of water you need to find out why this is happening. If it leaks all the time you may need a PRV to limit the water pressure in the house or the T&amp;P valve may be worn out and need to be replaced, and if happens only when you use hot water and the water is being reheated , you may need to have an  expansion tank installed to accept the expanded water as it is being reheated.