The asked for feature would need a package of its own, and in fact is the kind of things which would need a more structured document layout than LaTeX offers (which is but a slim layer on top of TeX) to its users. Nowadays probably LuaTeX offers the needed hooks into paragraph building.
Anyway here we go with poor man approach (an approach which does not even look into the way marginnote
package is implemented). Of course it has some rather severe limitations: one which comes to mind is the case of a paragraph split across two pages...
The \myparnote
must be used at end of paragraph in source.
As package marginnote
uses \pdfsavepos
etc... at least 2 compilations are needed.
\documentclass{article}
\usepackage{marginnote}
\usepackage{ragged2e}
\newcommand\myparnote[1]{%
\par
\xdef\zzz{\the\prevgraf}%
\marginnote{\smash{\parbox{\marginparwidth}{\RaggedRight#1}}}%
[-0.5\dimexpr\numexpr1+\zzz\relax\baselineskip\relax]%
}
\begin{document}
The command
\verb|\vadjust(filler){vertical mode material}|
is only allowed in horizontal and math modes (but it is not a (horizontal
command). Vertical mode material specified by \verb|\vadjust| is moved from the
horizontal list in which the command is given to the surrounding vertical
list, directly after the box in which it occurred.
\myparnote{Hello}
Any vertical material in a \verb|\vadjust| item is processed in internal
vertical mode, even though it will wind up on the main vertical list. For
instance, the \verb|\ifinner| test is true in a \verb|\vadjust|, and at the
start of the vertical material \verb|\prevdepth|=-1000pt.
\myparnote{I am here!}
The command
\verb|\vadjust(filler){vertical mode material}|
is only allowed in horizontal and math modes (but it is not a (horizontal
command). Vertical mode material specified by \verb|\vadjust| is moved from the
horizontal list in which the command is given to the surrounding vertical
list, directly after the box in which it occurred.
Any vertical material in a \verb|\vadjust| item is processed in internal
vertical mode, even though it will wind up on the main vertical list. For
instance, the \verb|\ifinner| test is true in a \verb|\vadjust|, and at the
start of the vertical material \verb|\prevdepth|=-1000pt.
\myparnote{Hi again,
it's me, and look how nice vertically centered I am.}
\end{document}
As the above illustrates, the OP left open some rather crucial questions about what was meant exactly by "vertically aligned", so we made a guess.

\section
or\paragraph
command.