Missing arduino bootloader problem?
No.  On Arduino-style boards which use distinct chips for the main processor (ATmega328p) and Serial interface (CH34x/ATmega8u2/ATmega16u2/FT2232 etc) the presence or absence of a bootloader on the main processor has no bearing on the recognition of a USB/Virtual Serial device by a host.

However on ATmega32u4 and some ARM-based boards it can.

Since you are describing a classic board with distinct chips, whatever your actual issue is, it is something else.