Yes, and indeed this is a very important issue. And the real serious part is - unlike what you've said, it may not, and perhaps even will not, be "painful". And the reason for that is that the perception of any sort of discomfort or pain, "over-stimulation", etc. can only happen if the eye is actually stimulated by the radiation in question. And by definition, these rays do not stimulate the eye, so it cannot react with pain. And this kind of intensity is very often encountered with lasers, and it is a significant safety hazard. In particular, if the laser is intense but at a wavelength the eye does not readily perceive, it may notice little to no light, and feel little to no pain, so none of the usual defensive reflexes will be triggered (including the all-important pupil constriction response) ... until that damage has already been done, which is often rather quick.
Now of course, not all wavelengths will affect the eye in the same way, as the eye's materials, like anything else, are not necessarily transparent to or respond to all wavelengths in the same way. In particular, if the radiation frequency is sufficiently low, so the wavelength sufficiently long and thus far into the infrared, it will not be able to reach the retina, but can still reach the cornea (the part of the eye that is on the outside of the lens) and cause damage there, which may not be immediately apparent but puts one at risk for cataracts. Indeed this can also happen with intense diffuse sources of such longer-wave infrared light as well with prolonged viewing, e.g. "glassblower's cataracts", due to the emission of infrared radiation from the hot glass, which is vastly more intense than the radiation in the visible (the "red/yellow glow" you see, which is usually not bright enough to itself be harmful - that requires much higher temperatures like those on the Sun. This can be seen from a graph of the Planck curve at suitable temperature - usually about 1400 K - although of course glass is not a great blackbody radiator given its transmissivity in the visible, but nonetheless it is especially opaque to far or long wave infrared (hence why that thermal infrared cameras need to be made with germanium lenses instead of glass lenses) and thus will be a better blackbody there.) but because of its long wavelength does not reach the retina, but instead the cornea, causing totally painless, YET HARMFUL, heating. A special infrared-blocking goggle is thus standard protective wear for this purpose, if one is going to glass-blow professionally and thus be exposed to this radiation on a long-term basis. (Lasers, due to their concentrated, monochromatic nature, will require different goggles - be warned and do NOT mix the two up, in EITHER direction, but ESPECIALLY not with lasers because their damage is instant, not gradual.)
In other words, YES you can be "blinded" (though not likely to be complete blindness, but get a "spot" in your macula and that can very well be effective blindness! And that's where you're most likely to get one because that's what you use to look at things!). And even worse, NO you might very well NOT feel pain until it's too late. And to answer your question about it "always appearing 'dim'" - yes, that's right - until it vanishes because it destroyed your retinal cells (for wavelengths that can penetrate the cornea and humours to reach the retina, that is) or at least stops getting "brighter" because your eye has been damaged just same but before the receptors gave off enough of a signal to tell your brain to perceive intense light. The radiation can't get bright enough to elicit a "bright" perception before your eye is damaged, often permanently, and often in the worst possible spot. The threshold for such wavelengths to elicit bright perception exceeds the threshold to destroy the receptors.
MAKE SURE TO PROTECT YOUR EYES with suitable goggles, ESPECIALLY with lasers - if you miss your goggles and you catch a beam in the eye that could be the end of your easy life and it's all the worse when those beams are invisible in every way (not even a visible spot on the wall, much less scattered light from air or suspended particulate)! And NEVER operate any remotely serious laser - that is, more than a laser pointer (which is ok so long as you DO NOT POINT IT IN your eyes) - without a good course in laser safety procedures.