Multiline syntax for piping a heredoc; is this portable?

Yes, the POSIX standard allows this. According to the 2008 version:

The here-document shall be treated as a single word that begins after
the next <newline> and continues until there is a line containing only
the delimiter and a <newline>, with no <blank> characters in between.
Then the next here-document starts, if there is one.

And includes this example of multiple “here-documents” in the same line:

cat <<eof1; cat <<eof2
Hi,
eof1
Helene.
eof2

So there is no problem doing redirections or pipes. Your example is similar to something like this:

cat file |
cmd

And the shell grammar (further down on the linked page) includes these definitions:

pipe_sequence    :                             command
                 | pipe_sequence '|' linebreak command

newline_list     :              NEWLINE
                 | newline_list NEWLINE
                 ;
linebreak        : newline_list
                 | /* empty */

So a pipe symbol can be followed by an end-of-line and still be considered part of a pipeline.