No. It will not work as a 50R load, rather it is 100R and you get twice the resistance and 4x the W capacity, not twice the power with four parts.
If the wanted twice the power, you only need 2x equal values. If you wanted 4x the power, your simulation would work at 50 Ohms using 4x 200R in parallel or 4x 12R5 in series might be possible , but only in theory as this is not a common value.
The sensible solution is your circuit with 50R parts. i.e. 1/4W in 2S2P array to handle 1W @ 50R.
Using N parts of equal value in symmetrical arrays gives you N times
the power capacity and the same resistance as the each resistor, because it is linear.
In the case of batteries and LEDs, you may increase the string voltage and current and increase
power capacity by N times using N EQUAL parts. The array you created is strings of 2 elements in
series with 2 strings in parallel, using standard notation would be
2S2P. The same notation is used with LED arrays and batteries to increase power in rechargeable batteries, with care taken to ensure they are equal at all times by design. E.g. Add ESR to LED's to "normalize" and limit current or add shunt limiters to large battery arrays to match each cell.