Legion has specifically debunked this for me for all time by actually going out and testing swimming like this just to put this to bed.
Swimming in any capacity in plate = no.
All righty I guess Ill post experiment details here then
A friend of mine is a dental hygienist (as well as one of the weirdest people ever). Over his time working he has collected (through what means I do not know) about a dozen of the lead-apron things used for Xraying. When plate armor swimming first came up, I was curious in an academic sense and I contacted him and we got working. We used about 5 aprons of different sections (about 5. It was hard to tell. He did the cutting/stitching/taping/assembly himself) and fashioned a piece that covered my torso, my legs to about mid-thigh, and my shoulders. My legs and arms were entirely unencumbered. The whole thing weighed about 25 pounds.
Now most of you probably don't know this but I am a swimmer. Its how I do my workouts. I swim everyday for an hour. Im not exactly athletic, but I felt that my skill in swimming in particular would account for the increased general athleticism a knight might have.
So I strapped the thing to me hopped in the pool and tried to swim.
First thing I tried was butterfly stroke. Butterfly impossible at any speed under any circumstance.
Next was back stroke. Similarly, back stroke impossible at any speed.
Next I tried free style. Freestyle possible, but problematic and scary as balls. The faster you go freestyling the easier it is to remain afloat, but I reached 100m sprint levels of exhaustion after about 13m. Furthermore, while doing freestyle I noticed consistently that my hips wanted to drop farther than my chest, making kicking difficult.
Next I did breast stroke. This was the easiest of the ones tried so far (but still damn hard). Breast stroke is already a slow stroke, and with the extra weight the vast majority of effort is put into staying above the water rather than going forward. I could consistently maintain above the level of the water but it took me 4.5 minutes to go 25m (for reference, I could normally do this in about 15 seconds.). At the end of this I was too tired to continue. However I strongly suspect that plate armor, while perhaps not horrifically encumbering on land for walking and running based tasks, would in the water make the leg motion for breast stroke all but impossible.
Lastly, I tried a non-conventional stroke which I created myself which I use when scuba diving. Conventional swimming strokes dont apply all that well with a tank strapped to your back.
This one was the most successful in terms of speed and safety, but it was the most exhausting.
The conclusion I gathered: this was with 25 pounds, literally no encumbering factors, and nothing but the (waterproof) lead apron apparatus. Increase the weight to 40 or 50 pounds, encumber the legs arms and head/neck, and any sort of cloth garment underneath and you are practically guaranteed a nice quick drown if the water goes above your head. The importance of the helmet should not be understated. Swimming with a device on your head is scary at best and horrifically debilitating at worst. A plate armor helmet is just about the worst thing I can imagine having on my head while swimming, right behind "live beehive." A particularly athletic man I suspect could, for a short while, maintain his position above the surface of the water. I do not believe anyone is realistically capable of swimming any significant distance at any respectable speed for any usable amount of time.