Way back during flight school one of the other students had been a radio operator in the Navy. He insisted you could tell a persons personality and even picture them like you can on a telephone. Is that really true?
Not really. Each person, especially with a straight-key has a distinctive "fist", say... An "accent". Their unique length of their individual elements of a character or even of whole words as you speed up above 13 WPM.
You can often tell WHO is operating a particular station, say a Club station where everyone's operating under the club callsign, by their unique on-air sound after you've heard it before, but I wouldn't say you could glean their "personality" or anything like that.
With the advent of keyers, bugs, paddles, and even computer keying and even copying with tools like CW Skimmer, and not many folks using straight-keys anymore, this is very difficult.
The "purists" don't like the tech, and like any other clique, can be found "brass pounding" away, in certain portions of the bands, just about any time of day. You can also find the computer-keyed/copied guys slamming away at 35 WPM or much faster intermixed with the "old-timers".
Common courtesy would dictate that if you get a call at a slower speed than you can operate, the other operator may be struggling and you should match the slowest sending speed.
If they still can't copy they might send a "QRS PSE" (Send slower please) to you, indicating their need for slower copy. It may not always be because they can't copy faster code, but because of local noise conditions, fading/warbling (common on "over the pole" HF paths), etc.
And some people won't slow down for anyone. So if that's a "personality" trait, perhaps.
But generally copying a personality? I don't think so.
You might tell if a person is a stickler for a well-operated station by things like key-clicks, chirping, warble of their frequency, etc... But that can also be a sign that they're struggling in the backwoods with an underpowered generator powering the station. Etc.
Some of these folks might be dimming the lights in their whole camp every time the morse key closes. The voltage drop can make for cool-sounding "sloped" elements the longer they hold the key down, and used to be common to hear from old tube-stations in South America, Cuba, Mexico, anywhere electrical power was not stable. Russia and the Soviet bloc too, back in the day.
Morse is losing out to a lot of nifty digital modes that base their roots firmly in Morse, but modern DSP technology allows these faster, forward-error-corrected signals to be copied by the DSP math so far down into the noise that a human simply can't hear them. Some specialized modes (like WSTJ) are built for meteor-scatter propagation (gotta be quick to bounce a signal off the ionization trails of meteors entering Earth's atmosphere) or moonbounce with exceedingly weak signals unless you have a giant dish and hundreds of watts at VHF, multiplied by the ERP of the antenna focusing almost all of that energy at the face of the moon.
I grew up right on the edge of the era where real teletype machines were still hooked to radios to do RTTY, and computers and homemade modems were taking over. In such, I still like RTTY but it's hard on radios with a horrendous duty-cycle and slow copy. I built my first two modems, one for RTTY and one for Packet/AX.25 from components on a breadboard and had a boatload of fun with both. Today, Ham Radio Deluxe software and a PC sound card interfaced to the radio will let you do those and a whole lot more for the cost of a couple of junkbox parts and a cable.
In fact, a friend and I spent an entire evening flipping through every mode we could on various digital modes just to try them out. It took all evening just to get through all of them.
My personal favorite radio interface for this stuff is the RigRunner USB, but computerized morse/CW and other digital modes can be done for virtually zero cost if you're on a tight budget.
Fun toys. Another expensive and time-consuming hobby. Right now most of my gear is gathering dust while I go flying on weekends.