If you let air escape through the nasal cavity during the oral closure, then yes--the first part of your /b/ is being articulated in the same way as an /m/.
This is not the standard way for native speakers of English to articulate stop consonants. If a native speaker actually (phonetically) voices her stops (i.e. if there actually is vocal fold vibration during the oral closure), the vocal fold vibration is achieved by passing the air through to the oral cavity only. This is possible even when the oral cavity is completely sealed (due to the lips being closed, for example) because the air is a gas and is thus compressible. The walls of the cavity may also expand a bit to accommodate the greater volume of air. You can convince yourself that this is true if you hold your nose shut with your fingers and attempt to "hum" with your lips closed.
It is true that maintaining vocal fold vibration with both the oral and nasal cavities closed is difficult. This difficulty, along with the fact that there are more robust cues to (phonological) voicing in English (see my response to a related question), explains why many native speakers don't actually phonetically voice their voiced stops! If you record someone with consistent stop voicing and then go in and replace all of the voice bars with silence, all of the stops will still be perceived by other native speakers as voiced.