The quick answer: May work just fine if their is decent number of fish respirating CO2, or else nutrients could buildup and cause issues or be wasted. The EI 50% WC is good for keeping a buildup from happening. Whether ferts are even needed depends on the rest of the setup. lighting, stock etc. If the plants are growing healthy and fairly fast on any tank, CO2 or not, they are going to need to get some food from somewhere.
The convoluted answer I typed out first:
Depends, anything is possible. But there is a point where a lack of one nutrient (CO2 included) will render the plants unable to take complete advantage of another, resulting in a buildup of nutrients in the water column. In this case, EI is a good way to keep a handle on nutrient buildup that isn't being consumed by plants, but it is still a waste of money on fertilizer that eventually goes down the drain. Whether a tank succeeds or not this way really depends on how much and what type of light it has, low light = no ferts or CO2, high light = consistent ferts and CO2, and how it is stocked, lots of messy fish = more CO2 and nutrients already present, no fish = little to no naturally occurring nutrients and CO2 is in equilibrium with the atmosphere. All must be balanced whether it's covered by fish respiration and waste or by you adding it. IME, a tank that is left on it's own (no added cO2 or ferts) usually fully
establishes after 6mo or so, give or take (longer than the typical time frame of establishing a nitrogen cycle) and can certainly appear to be injected and dosed when in fact it's not, but growth is slow and problems came and go in slow fashion, so patience is key, sometimes total ignorance and disregard for husbandry (ignoring the tank) gives great results as nature tends to have all the patience and grace about doing things until we start monkeying around and throw a kink in the process. This tank could have a low to moderate level of light to stay in balance with the lower levels of CO2 and nutrients, or could have a high level of light if fish and husbandry can keep other levels up and balanced with the light level.
On my high light tanks, the first thing I usually see when CO2 falters is algae, either black brush or green hair.
Some people like Tom Barr are dispelling some myths of certain nutrients inducing algae, but IME, if you already have a bit of algae from an ammonia spike, cross contamination, whatever the source is, then an excess buildup of nutrients in the water column can certainly assist the spread of certain algae, especially if the plants aren't given what they need to flourish and out-compete it. This is something one needs to consider -whether or not the plants are growing well enough without CO2 injection to even need fertilization-. Possible misconception is that dying plants need ferts and healthy pearling plants don't, when in fact the healthy plants do need a consistent source of nutrients, wherever it's coming from, or else their increased uptake will strip the tank of nutrients and cause issues, dying plants may or may not need the addition of a certain nutrient depending on the case, light and CO2 included, but randomly dumping dry ferts in to save dying plants is not always necessarily the answer to th problem. EI is a smart way to keep those nutrient values in check with the weekly 50% WC, but IMO it's wise to get consistent CO2 in check before adding heavy light or fertilizer, preferably planned out and all started at the same time (though that's easier said than done for people just starting out, time and experience brings them to this realization too).
My opinion of a properly started planted tank;
1. Solid source of H2O with steady parameters -check-
2. Steady CO2 -check-
3. All nutrient values in proper range and on hand for dosing -check-
4. Proper lighting spectrum and wattage -check-
5. Tons of fast growing plants -check-
(2 & 3 either covered by decent stocking or human addition)
(2, 3 & 4 partially dependent on what the owner's plans are for the tank, ie high tech/low tech)
(aside from fish, a rich substrate can supply much of the needed nutrients in a low tech tank)
is it really still helping all that much?
It is if the plants aren't getting their nutrients from some where else, they still need something to grow on whether the tank is low tech or high tech, they may just not need it that often or at all if the fish or substrate can cover it. I would definitely feel safe having the EI method's 50% WC if I felt the need to religiously dose ferts into a tank no matter what the case was with the CO2 etc, or I would just go lean on ferts or skip them all together if it was a low light/no CO2 tank with slow growth.