Okay, first of all, I want to thank everyone who responded to my initial post!
Assuming that sleep mode does to f-up the COM port connection, I uploaded the following:
int led = D10;
void setup() {
pinMode(led, OUTPUT);
esp_sleep_enable_timer_wakeup(2000000);
}
void loop() {
digitalWrite(led, HIGH);
delay(100);
digitalWrite(led, LOW);
esp_light_sleep_start();
}
Lo, and behold, I get an led that blinks every two seconds!