The environment of AmsLaTeX are being scanned as parameters of \collect@@body. Hence, the featured of TeX4ht introduced to \halign are nulled there.
<..equations of amsmath.sty..>+
\catcode‘\#=13 \catcode‘\!=6
\def\reg:multline!1{%
<.inany@true.> \Let@
\@display@init{\global\advance\row@\@ne \global\dspbrk@lvl\m@ne}%
<.displaybreak@.> \restore@math@cr \let\tag\tag@in@align
\global\tag@false \global\let\raise@tag\@empty \mmeasure@{#1}%
\let\tag\gobble@tag <.multline label.>%
<.halign amsmath multline.>}
\catcode‘\#=6 \catcode‘\!=12
-_-_-
<..halign amsmath multline..>
\ifst@rred
\expandafter\let\csname e:multline*\endcsname=\empty
\expandafter\let\csname f:multline*\endcsname=\empty
\fi
\SaveMkHalignConf:g{multline\ifst@rred *\fi}\HRestore\noalign
\MkHalign#{\hbox{$\m@th\displaystyle<.sub/sup base.>#$}}!1%
-_-_-
<..multline label..>
\ifst@rred \let\label\@gobble \else
\stepcounter{equation}%
\def\label{\let\cnt:currentlabel\@currentlabel
\def\:@currentlabel{\ifx \cnt:currentlabel\@currentlabel
\the\c@equation\else \@currentlabel\fi}%
\anc:lbl r{equation}\ltx@label}%
\edef\@currentlabel{\the\c@equation}%
\fi
-_-_-
<..multline tag..>
\ifst@rred\else
\e:multline\csname a:multline-num\endcsname
\tagform@\theequation\csname b:multline-num\endcsname\f:multline
\fi
-_-_-
<..equations of amsmath.sty..>+
\def\:tempc{<.multline tag.>\math@cr \EndMkHalign
\RecallMkHalignConfig \csname b:multline\ifst@rred *\fi\endcsname
$$\global\@ignoretrue }
\HLet\endmultline=\:tempc
\def\:tempc{\pic:MkHalign{multline\ifst@rred *\fi}}
\HLet\multline@=\:tempc
\NewConfigure{multline}{6}
\NewConfigure{multline-num}{2}
\@xp\let\csname reg:multline*\endcsname=\reg:multline
\@xp\let\csname endmultline*\endcsname=\endmultline
\NewConfigure{multline*}{4}
-_-_-