It's hard to discuss this topic without knowing for certain if Di Vinci actually died of a stroke (remember, strokes would be hard to diagnose at that time given their understanding of the human body). Assuming he did, I don't see how that particular sleeping pattern would have lead to a stroke in any way, unless he experienced some sort of disturbance, like sleep apnea, which leads to low oxygen levels being delivered to vital organs. Now, according to the study referenced below:
REM sleep—occupying about 20% of total sleep—is dominated by marked fluctuations in sympathovagal balance (irregularly peaking sympathetic surges against a background of tonic vagal inhibition), which lead to abrupt changes in blood pressure and heart rate.
Hence, if you have a condition like sleep apnea, this type of sleep may be disrupted. Poor health could cause a stroke while sleeping if you have high blood pressure or poor dieting.
A compromised cardiovascular system is at risk for pathological events such as myocardial ischemia or arrhythmias during REM sleep
Please read this part on sleep fragmentation:
Any causes of sleep curtailment, including sleep restriction, insomnia, and shift work, are likely to impair cardiovascular restoration through a reduction in cardioprotective stable NREM sleep. Sleep fragmentation, conventionally defined by cortical EEG arousals, is a universal feature of almost all sleep disorders, including sleep apnea, insomnia, periodic limb movements during sleep (PLMS) and narcolepsy, and is associated with overshoots in sympathetic activity [25,26]. Even if REM sleep is preserved, the greater the sleep fragmentation, the farther the sympathovagal modulation is tilted toward sympathetic dominance [27]. Blood pressure regulation during the biological night (the usual sleep time) is uniquely related to cardiovascular risk, including the risk of stroke [28-30]. Non-dipping—loss of the typical blood pressure drop during sleep—is associated with a host of poor cardiac, neurological, metabolic, and renal outcomes [31-36]. Sleep fragmentation causes non-dipping [37-40]. Non-dipping is common in older adults and is associated with an increased risk of stroke [41-43]. Reduced dipping is associated with brain atrophy, worse functional status, and lower daytime cerebral blood flow [44,45].