Can Gravity Guy Make It?

Snails, 15 bytes

Try it online?

^
\ n\ ,=\#r}+~

​​ ​ ​ 0​. ^ is an option that requires the pattern to start at the top left.

1. \ ​: match space

2. n: Turn 90 degrees in either direction

3. \ ,​: match space zero or more times

4. =\# check that there is a # in front of us

5. r: set the direction to right

6. }+: do all of the preceding one or more times

7. ~ match a cell which is out of the grid bounds

Perl, 93 89 81 77 76 75 74 bytes

Includes +2 for -0p

Run with the input pattern (with all lines space padded to the same length) on STDIN:

gravity.pl < gravity.txt

gravity.pl:

#!/usr/bin/perl -0p
/
/;$n=".{@-}";s/#$n\K( $n)*\b |(^|w)([w ]$n)*\K $n#/w|$&/es&&redo;$_=m;w

This file based version needs the final newline, so that is really 75 bytes. But the commandline based version doesn't need that extra newline so this counts as 74 bytes:

perl -0pe '/
/;$n=".{@-}";s/#$n\K( $n)*\b |(^|w)([w ]$n)*\K $n#/w|$&/es&&redo;$_=m;w' < gravity.txt

Explanation:

This will construct a string with a w in each positions gravity guy can reach. So for the second to last truthy example it will construct:

     #########   
    ##### ####   
   #wwwww#wwww#  
  #w  # #w ##ww# 
wwwww wwwwwww#ww#
#####  ####  w#ww
     wwwwwwwwww# 
     #########   

So gravity guy can make it if and only if there is a w in the last column. The string will be constructed by replacing one reachable space by w in each round.

Each replacement will be of the form

s/prefix \K space postfix/ w | $& /e

which will demand that the space is preceded by prefix and followed by postfix but replace only the space by w without needing lots of advanced grouping.

Assume $n contains a regex that will progress just enough that the left and right sides are exactly below each other. Then the relevant regexes are:

/^( $n)*\K $n#/       From the first position drop down as long as you
                      encounter spaces until you encounter a #. 
                      This puts gravity guy on his starting platform

/#$n\K( $n)*\b /      A space immediately below a # and if you (optionally)
                      go down further from there (as as the descent is
                      over spaces) you get to a space that follows a word
                      boundary. The only way to get a word boundary is if 
                      there is a w in front of that space. This selects the
                      position gravity guy ends up on if starting from that
                      w and gravity is up
/w([w ]$n)*\K $n#/    A w followed by a space (or w) and if you go down from
                      there as long as it is over spaces (or w) you finally
                      end up on a space directly above a #. This handles the
                      gravity down case. The test uses "space or w" instead
                      of just space to handle this case:

                       #
                      ww
                      #x  
                       #

                      Position x is currently a space and must be replaced by a
                      w but the gravity up regex has already put a w directly
                      after the w gravity guy takes off from. So for gravity
                      down we must handle w as if it is still a space. This
                      is not needed for gravity up because regex always matches
                      starting at the earliest possible character, so 
                      gravity up matches before gravity down

With that out of the way the program is easy:

#!/usr/bin/perl -0p   Slurp all of STDIN into $_, at the end print $_

/\n/                  Match the first newline (needed to measure the row
                      length)
$n=".{@-}"            $n effectively becomes rowlength-1 times ".". This
                      will be the regex that goes one step down a column

s/#$n\K( $n)*\b |(^|w)([w ]$n)*\K $n#/w|$&/es

                     This is the 3 regexes shown above combined. The s 
                     modifier is needed so the . in $n also matches newline

    &&redo           Keep looping as long as w's keep getting added

$_=m;w\n;            Check if the last column contains a w: He made it!
                     The \n; at the end is not written. These 2 bytes sneakily
                     come from the -p option for the ; and the -e option
                     for the \n

JavaScript (ES6), 174 bytes

a=>[...a[0]].map((_,i)=>[...t].map(x=>s[x]<'#'&&g(s.indexOf('#',x),-1)&&g(s.lastIndexOf('#',x),1),s=a.map(s=>s[i]),t=new Set),t=new Set([0]),g=(i,d)=>i<0||t.add(i+d))&&t.size

Takes a horizontal array of strings and returns the number of exit points. Transposing the array costs me 29 bytes. Ungolfed:

function gravity(array) {
    var set = new Set;
    set.add(0); // starting point
    for (var i = 0; i < array[0].length; i++) {
        var s = array.map(s => s[i]); // transpose array
        var old = set;
        set = new Set;
        for (var x of old) {
            if (s[x] == '#') continue; // hit wall
            var j = s.indexOf('#', x); // try downward gravity
            if (j >= 0) set.add(j - 1);
            j = s.lastIndexOf('#', x); // try upward gravity
            if (j >= 0) set.add(j + 1);
        }
    }
    return set.size;
}