not by default and/or easily…
Be aware, depending on the option you select, it might void your warranty.
First, these NAS devices have Debian Lenny distribution, so LOTS of options out there. However, due to it, Linux experience and/or willingness to learn/research/test/etc is necessary. In a nutshell, this would be necessary:
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Access MBL via SSH
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Create a web server/site, add your content
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Access from the internet such as port forwarding and DDNS
If still interested, do the above steps one at a time, baby steps.
and last, I am not a Linux expert nor I have ever done this!!!
I can, however, point you to a place with lots of info:
http://mybookworld.wikidot.com/mybook-live#toc1
Pay attention to “Others tools specific to MyBook Live”.
Other options mentioned on this forum…
Beautiful Directory Listing for Apache File Server Sharing Public Folder