Typographically, this is not recommended, unless you want to go back to the days of typewriters. However, here is a solution. It ises the fact that the last mandatory argument of \titleformat may end in a command with an argument which will be the section title. You may or may not want to underline the labels and section titles, or only section titles:
A solution to underline only section titles:
\documentclass[11pt, a4paper]{article}% http://ctan.org/pkg/amsproc
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{soulutf8}
\usepackage[]{titlesec}%
\titleformat{\section}
{\Large\bfseries}
{\thesection.}
{0.33em}
{\ul}
\begin{document}
\section {The History of the Seven Families}%
In former days – that is to say, once upon a time, there lived in the Land of Gramblamble, Seven Families. They lived by the side of the great Lake Pipple-popple (one of the Seven Families, indeed, lived in the Lake), and on the outskirts of the City of Tosh, which, excepting when it was quite dark, they could see plainly. The names of all these places you have probably heard of, and you have only not to look in your Geography books to find out all about them.
\end{document}[![enter image description here][1]][1]
A solution to underline labels + section titles:
This code underlines labels and section titles:
\titleformat{\section}
{\Large\bfseries}
{\ul{\thesection.\enspace}}
{-0.15em}
{\ul}

environpackage allows for an environment body to be captured in a macro,\BODY, which can then be used (when properly expanded) in a braced form. – Steven B. Segletes Oct 01 '18 at 18:24\bfshould be\bfseries. Furthermore,\bfseries(or\bf) are not environments, but declarations, that continue until explicitly turned off, or until the end of the group. – Steven B. Segletes Oct 01 '18 at 18:28\bfseriesin terms of\textbf, whereas\textbfcan be more or less trivially defined in terms of\bfseries(\newcommand\textbf[1]{{\bfseries #1}}(the actual definition is slightly more complicated but not much. – David Carlisle Oct 01 '18 at 19:01