There are a few problems with your plan.
First off. If you're going to make a heat exchanger, you should use copper instead of PEX. Copper has a thermal conductivity of 401 watts/meter kelvin (W/mK), while PEX is closer to 0.51.
The next problem, is the volume of water you're preheating. 1" PEX has an inside diameter (I.D.) of just 0.865". Which means 100' of PEX, can only hold 3.0527478 gallons of water.
Volume = pi * r^2 * L
V = pi * 0.4325"^2 * 1200 in.
V = pi * 0.18705625 sq. in. * 1200 in.
V = pi * 224.4675 cu. in.
V = 705.18544896966691375461340363629 cu. in.
One cubic inch can hold 0.004329 gallons of water.
X = 705.18544896966691375461340363629 cu. in. * 0.004329
X = 3.0527478085896880696437214243415 gallons
In the US, shower heads are limited to a maximum of 2.5 gallon per minute flow rate. Which means if you're taking a shower, the preheated water will be used up in just over a minute. Even if you were to use 100 ' of 1" Type M copper tube, you'd only have 4.5411268397 gallons.
V = pi * 0.5275 in.^2 * 1200 in.
V = pi * 0.27825625 sq. in. * 1200 in.
V = pi * 333.9075 cu. in.
V = 1049.0013489785338857719650955024 cu. in.
X = 1049.0013489785338857719650955024 cu. in. * 0.004329
X = 4.5411268397280731915068368984299 gallons
That would almost give you a two minute shower. Though even with the higher thermal conductivity of copper, I doubt the incoming water would be able to pick up enough heat to make a difference.
This is why using a 40 or 50 gallon holding tank is preferable. At 2.5 gallons per minute, you could take a 16 minute shower with just the water in the 40 gallon tank.
Insulation is your enemy
Modern hot water tanks are designed to retain heat, and are well insulated to do so. If you're using an off the shelf hot water tank as your holding tank, this insulation is going to work against you. You'll want to remove as much of the insulation as you can.
Contamination, Pressure, and disease
To prevent contamination into the water supply, you're going to want to install a check valve on the supply line feeding the holding tank. Because heating water increases its volume, you're going to have to install an expansion tank between the holding tank and the heater. Finally. Standing water is a breeding ground for bacteria, so you'll want to make sure you heat the water to at least 140°F (60°C).