I think I found a solution without modification of the syntax-table.
From the GNU Emacs Manual - Sect. 35.7 Abbrev Table Properties:
If this property is nil, the default is to use backward-word and forward-word to find the name. This property allows the use of abbrevs whose name contains characters of non-word syntax.
I.e. it is only the default behaviour that non-word syntax is used to define the abbrev "boundaries", but this can be configured.
(abbrev-table-put org-mode-abbrev-table :regexp "\\(\\\\[a-z0-9@]+\\)")
lets me insert abbrevs with leading and trailing slashes in
org-mode. (For other modes, or globally
org-mode-abbrev-table needs to be replaced accordingly)
(With help from reddit: https://www.reddit.com/r/emacs/comments/3pi8wx/abbrevmode_expansion_with_trailing_does_not_work/ )