Searching for a string in a downloaded PDF
First of all standard library imports and third-party library imports should be kept separate:

from subprocess import PIPE, Popen
from urlparse import urljoin

import mechanize


It's better to put your code in a function so that you re-use it with different urls, search keywords etc. Further explanation in comments:

def pdf_contains(url, file_url, search_key, keyword=''):
    br = mechanize.Browser()
    br.open(url)
    print br.title()
    # As you're interested only in the first link text that contains
    # the keyword('Sunday,' in this case) we should better use next()
    # with a generator expression. `next()` will yield the first item from
    # the generator if any otherwise we'll return None
    # Also `urlparse.urljoin` can come handy in joining urls.

    pdf = next((urljoin(file_url, f.url) for f in br.links()
               if keyword in f.text), None)

    # Now instead of downloading the file using .urlretrive we 
    # can simply simply get a file-like object using
    # `mechanize.urlopen` which then we can then pass to
    # subprocess's STDIN 

    if pdf is not None:
        data = mechanize.urlopen(pdf)

        # Now instead of running `os.system` and storing the output
        # in a file we can use `subprocess.Popen` to store the
        # output of ps2ascii command in PIPE

        proc = Popen(['ps2ascii'], stdin=data, stdout=PIPE)

        # Now simply read the data line by line from PIPE
        # and check for the search_key, if found return instantly 
        for line in iter(proc.stdout.readline, ''):
            if search_key in line:
                return True
    return False

url = ("http://sttm.org/Bulletin/Bulletins2015/tabid/483/Link"
       "Click.aspx?fileticket=WkjzL8SuMQQ%3d&amp;tabid=483&amp;portal"
       "id=0&amp;mid=979", "http://sttm.org/Bulletin/Buletins2015/")

scheduled = pdf_contains(url,
                         "http://sttm.org/Bulletin/Buletins2015/",
                         "My Name Here",
                         "Sunday,")

print scheduled