How to tune a radio receiver using a crystal oscillator?
"...Will the oscillator actually emit a signal that can be picked up by the receiver?"
Yes.  You don't even need a frequency marker, if you can hear the signals that you want.  

You should just read on in the instruction manual.  It seems quite clear and my answer would just repeat what the manual already says.  Here is a quote.  


  Alignment:
  Turn on whatever reference signal source you plan to use. This can be a 
  regular transceiver keying a few milliwatts into a dummy load, a crystal 
  oscillator or a signal generator. Or, you can look for a known signal that you 
  have tuned in on another receiver. 
  If you are without any reference signal whatsoever but have a reasonable 
  antenna , you can use your familiarity with the 40-meter band to make a 
  rough alignment of the receiver.If Ham radio and 40 meters are new to you, 
  here’s a rough idea of what you can expect to hear on this busy band. 
  7.00 - 7.08 MHz - CW, most of it is fairly fast 
  7.08 - 7.15 MHz - Teletype (RTTY) and digital operation 
  7.10 - 7.20 MHz - SSB voice, many different languages 
  7.20 - 7.35 MHz - general SSB voice operation