Yes, trace quantities of methanol in ethanol (as opposed to say ridiculous quantities like 40-60% in some denatured alcohol brands), in the context of potable alcohol but of lesser quality would indeed just lead to a shittier hangover, at worst, cheapo vodka etc. that they probably really skim a bunch of the heads from the distillation off until it fulfils the requirement for not having acute methanol toxicity, refractionate as much as possible once they build up enough and toss it back in.
The difference between bottom of the barrel toilet cleaner shite like 'glens' and something like grey goose or russian standard is pretty huge. Before fomepizole (an alcohol dehydrogenase inhibitor) was available, the emergency hospital treatment would be to saturate the enzyme with ethanol, since its not the MeOH itself that does the damage but the formaldehyde and formic acid (rather than acetaldehyde, still fairly unpleasant stuff, granted but lacks the acute toxicity in levels built up in getting intoxicated.)
In other words, suspecting methanol poisoning, they'd get the poor bastard so blind fucked up drunk, that there would be no or little available available alcohol dehydrogenase to produce formaldehyde, due to its being tied up producing acetaldehyde. So they'd end up with the sort of hangover that might itself just about constitute a medical emergency itself

but at least would spare the optic nerve, danger of lactic acidosis and other physical damage.
Sod it, I fancy getting really drunk now (and already ON an alcohol dehydrogenase inhibitor as it happens) Although it is meant to be completely un-denatured, with the non-EtOH remainder being 5% or so of water. Originally got it for Beaveault-Blanc reductions (where a suitable substrate is reduced using sodium in anhydrous ethanol, such as for example an oxime to an amine. And was sold for needs where methanol is specifically unsuitable (such as many things involving borohydride, which is a lot more stable in EtOH than it is in methanol, such as for, say, preparing one of the two kinds of Ni2B nickel boride reduction catalysts, MeOH can be used to prepare the P2-type (P1 is the other type, which is prepared in aqueous solution, similar to raney nickel although nonpyrophoric, and with less tendency towards causing chiral inversion on sterochemically-sensitive materials than raney nickel by a few orders of magnitude) but seems no good for the actual reaction solvent itself due to the low stability of NaBH4 in MeOH.)
Might just give a small shot a go. Diluted somewhat mind you, just washed the hell down quickly, I rememer what too much absinthe did to my throat after drinking an entire bottle of the stuff.
Hmmm, tasted alright and didn't burn that much when it was diluted with some (neat) sugary elderflower cordial mixture and followed by a long chaser of H2O/elderflower cordial solution. Burnt a lot less than vodka. But Bozhe Moi! (since this is russian afterall, most of the lettering is in cyrilic, IMO that is apropos :D easiest to read is 'ethylic spiritus' that I'm feeling first alerts of intoxication within perhaps 60 seconds or less. Not going to drink more than the one shot. But fuck me sideways, no need to. Measured out about an inch or two high in a small teacup and slugged it down. Less burn than dilute EtOH, was mistaken about the smell though, that was just when working with it, actually putting my nose to the bottle, bloody 'ell, that itself is enough from half a cm away to knock your nose into next year.)
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Frustrating though really. I need it DRY, not merely 95% and atm ALL its suitable for is drinking or perhaps some reduction protocols employing either NaBH4 or Ni2B/borohydride.
Still waiting for my several Kg of cacium oxide (quicklime) and calcium carbide, and to be able to afford some lithium aluminium hydride or Red-Al. (both actually since I need at least a small amount of the exquisitely sensitive Red-Al for a very small quantity (a mere few single digit range grams) of what may prove to be a highly sensitive substrate that both may well never become available ever again and cost almost £100 for just 5g, so both my two projects with that need it, those MUST be got right to a degree that'd have made Sasha Shulgin weep for joy (put it this way I'm prepared to expend thousands just to practice the chemistry field) involved just before this particular experiment)'
Results from the EtOH-woke about 5-6 hours later with just the BAREST memory of entering drunkenness, Even diluted a bit by flavoring that stuff packss a fucking kick, Went straight from 'fingers slightly incoordinated on computer keys' to blackout and 6 hours later waking up. (should add, I take a drug known for enhancing the potency of ethanol, chlormethiazole, for seizure prophylaxis. BUT thats a lot more potency enhancement than I'd expect, being pretty much intimately familiar with the latter by now) stuff was bloody strong, strongest EtOH I've ever had, no hangover so far at this dose.