Doable? Sure, sort-of.
A 'good' plan? Not really, IMNSHO.
Usage of compressed air depends on two main factors, the pump to make the compressed air and the storage tank(s) to store that compressed air until use.
The duty cycle of the pump/motor combination is (usually) matched up with the general usage envisioned
and the air storage capacity of the tank.
So a small pancake or hotdog compressor unit made to run a small brad or finish nailer can have a relatively small motor to run the relatively small pump that fills the relatively small air tank in a 'reasonable' amount of time and runs the pump/motor within their (usually 50%) duty cycle so that they don't overheat and burn-up/fail.
Take that same, perfectly adequate to run a brad nailer, unit and try to continuously run a high-demand air tool like maybe a die grinder or DA sander or large(r) spray gun or media blaster and you just don't have enough pump or motor or air tank capacity to run the tool(s) properly or for very long at all.
You just can't add more air tank capacity, because you still have the original 'small' pump/motor trying to fill up the larger volume of tank capacity. Result is that the pump/motor runs longer trying to fill the bigger tank(s) and overheats (either just a little bit or a whole lot ending in a burned up pump/motor.)
More air tank capacity lets you use a high-air-demand tool for a brief period of time before the tank runs out of air. Then you have to wait for the pump to refill the tank and then you briefly use the air tool again. example: an impact wrench. Those handy beasts can **** down air at greater than 20 CFM (medium-to-heavy duty 1/2" impact wrench) but are often used for just a short burst to tighten/loosen the fastener. So while you move over to the next fastener, the pump can be refilling the air tank. If you are continuously running the impact, not many 'homeowner' sized air compressors can keep up with that sort of air demand on a non-stop basis.
Also, related to the above mentioned gotcha about those small 'portable' air tanks not having a drain valve, is that all of the ones I've seen also have a limited design/use pressure limit of just 125 psi and those tanks also have (or are supposed to have, based on the thinner tank wall metal and the lower design pressure and the lack of a tank drain) a mandated 'short' shelf/use life of IIRC either 5 or 10 years. Yeah, those portable air tanks are supposed to be scrapped after just 5-10 years.
Next, let's look at the math for a minute. Say six 5-gallon tanks at $40 each. That's $240 for 30 gallons of tank capacity. Add in another say $10 in fittings and pipe runs per 'unit' (a T fitting for each, plus some elbows and drip legs and adapters to get all the pieces to connect, oh and some drain valves on each drip leg and some isolation valves so you can shut off just a tank or two if they have a problem or whatnot, and I easily see $10 in parts costs per 'unit' to rig things together, unless you happen into a 'deal' on all the fittings and piping and valves and so forth) and you have another $60 in piping costs for those five small tanks all manifolded together.
So that's ~$300 to rig up 30 gallons of tank storage capacity.
A brand-new, full retail price, 'industrial' supplier Grainger has a 26 gallon 175 psi ASME horizontal tank at $551. Inlets, outlets, drain.
https://www.grainger.com/Grainger/SPEEDAIRE-Air-Tank-1TZZ4
And no matter what, you still have to have a compressor pump and motor and rig all that up.
It's usually simpler to just go and buy a 'decent' air compressor unit with the pump and motor already sized to the tank capacity and the entire unit picked to meet your 'needs'. (btw, try to more CFM capacity than you think you need. Air tools can make your life and 'chores' go faster and easier, but only if you have enough CFM capacity to 'feed' them.)
Most of the time, for a home hobby/shop, a 60 or 80 gallon unit (with the 3 or 5 hp electric motor) is enough for -most- tasks. Overkill for filling up a bicycle tire and might not be quite enough to run a 'big' media blaster or other really air-hungry tool. YMMV.
Determine what air tool(s) you want to run. Find a compressor unit (pump and tank) that will meet the CFM demands to run those air tool(s) and meets your price/quality/durability point.