Yes, multiple MSG files can be converted to EML with attachments, but it is better to do it with a careful process. If the emails came from Outlook, keep all MSG files in one folder first. This makes selection easier and avoids missing any file.
A free way is to open each MSG file in Outlook and save or move emails one by one but this is slow when there are many files. It also depends on Outlook being installed.
For bulk work Softaken MSG to EML Converter can be used as a simple option. It converts multiple MSG files to EML or EMLX , keeps attachments and supports HTML, RTF and plain text emails. You can also choose selected MSG files and save the output in a new or existing folder.
Tip: try the free demo on a small set first and compare a few attachments after conversion.