A great deal has been said and written on this, but the best reference is John Deakin's articles which can be found at avweb.com (they keep moving about on there...)
The short answer to the original question is NO.
Both carburetted and fuel injected versions of the standard Lyco/Conti aircraft engines have their fuel metering set up so that when all 3 levers are fully forward at sea level the engine will develop its full rated power, and the mixture is then very rich, setting the engine operating point at about 125F rich of peak (ROP). This results in a lot of unburnt fuel, which gives cooler combustion.
It's done because these lightweight engines are poorly designed when it comes to removing excess heat, and their air/fuel flows to different cylinders are usually poorly balanced so one has to waste fuel to the cylinders with the richest mixture to avoid those with the leanest mixture not getting enough.
If you now start to lean the mixture (still at full throttle) the EGT starts to rise, the CHT will rise, but the engine won't be producing any more power. The worst point heat-wise is about 50F ROP.
If you continue leaning, to peak EGT, the fuel is being burnt with exactly the right amount of air and this is the most efficient operating point (actually it happens about 25F LOP (lean of peak) but it makes no practical difference). Lyco engines are in general authorised to run at peak EGT at 75% of rated power or lower only.
Then if you continue leaning into the LOP region, the power output is more or less proportional to the fuel flow rate. This is a good place to be. If the engine was really well set up (every cylinder getting the same amount of fuel etc) then you could just leave the throttle on full bore and use the mixture to control the power... in practice fuel and air flow imbalances cause excessive vibration and many engines can't run in the LOP region (this is where GAMI injectors come in; you buy a set matched to your particular engine).
That's the essence of it.
Getting back to the original question, if you lean to about 50F ROP and leave it there, with the throttle on full bore, climbing at Vx (i.e. not a lot of cooling) and let the CHT rise to 500F or so, you will probably get detonation and eventually knacker the engine. Detonation is not usually evident to the pilot - other than through a rapid rise in CHT. (Pre-ignition is evident but that's an altogether different thing.)
So, a "little leaning" is not a good idea. Best to climb with everything forward (as the POH says) to either
a) top of climb, or
b) to an altitude where the power will be below 75% (due to loss of air)
and then set the plane up for cruise and lean to peak EGT, or a little bit LOP if you can.
If your engine is poorly balanced and can't reach peak EGT without shaking too hard, then you are bit stuffed..... you have to run the engine with a very rich mixture.
On the plus side, Deaking suggests that one cannot achieve detonation unless the CHT is above about 450F and 75% power (this was a TIO540 test I think). This suggests that one isn't actually going to damage the engine by incorrect leaning at any "normal" cruise setting.
I fly an IO540 and do exactly as above; all 3 forward to TOC or to about 6000ft, then set 23/2300/LOP (10.5GPH) which is about 60-65% power, and just sit there. Leaning a little bit more if climbing higher, to maintain peak EGT.