You can
import as many MSG files into Thunderbird all at once. However, Thunderbird cannot open MSG files right out of the box. You must first convert those MSG files into a format supported by Thunderbird, such as EML or MBOX. The easiest way to do this is with a converter tool like
Mailvita Converter for MSG. This tool allows you to convert multiple MSG files in batch mode into either EML or MBOX formats and preserves the email content, attachments and formatting when doing so. After converting the files you can then easily import them into Thunderbird. This software is very user-friendly and has a free trial so that you may evaluate it before you buy it.