The screen on an etrex is too small to show OS detail and that would rule it out for me.
While, almost paradoxically, the OS map is too lacking in detail to be useful on an eTrex.
I've tried the OS 1:50k mapping on my eTrex 30. It's very occasionally useful, in that way that only an OS map can be. But most of the time it's hopeless, because the map is a bitmap that only really works at 300m zoom or less, which means you don't have enough precision for knowing eg. which of two adjacent turnings to take. Also, being a bitmap OS map, it only really works properly in 'north up' mode, which doesn't make the best use of a portrait-aspect screen. The rendering is also tediously slow, but that's largely offset by the low zoom level.
For most practical purposes, an OSM-derived vector map (or for on-road use the old City Navigator maps) is usually superior on an eTrex-like device. For 'big picture' stuff I use OS maps in Viewranger on a 10" tablet.
But I don't think a map actually matters for geocaching, because - by its very nature - you already have precise coordinates for the point you're trying to get to. All a map can usefully add is how to get from where you are to that point when there's an obstacle (fence, river, hedgerow, cliff edge, etc) blocking the direct route, and - at least in the early days - finding your way around that sort of stuff when all you had was an arrow saying "327m that way" was a large part of the fun.
The eTrex is an excellent unit for walking and geocaching, as it's a sensible handheld size, rugged, and the AA batteries last for ages. Which by no coincidence is why I own one for navigating and recording bike rides. And when I first tried geocaching, one of its predecessors was the only option, because pocket computers didn't have built-in GPS, telephony or cameras in those days.
I've never actually played with the eTrex's geocaching-specific features. I assume they amount to a special form of POI with geocache descriptions included, or something. Probably means you have to use Garmin browser plugins or something Windowsy to upload them. If the modern stuff can talk to a smartphone via Bluetooth, then all the better.