Yes, If you hold the plug to the engine...make sure it is grounded metal and not on a rubber mounted cover or something (cooling fins work well...and away from the spark plug hole so you don't accidentally ignite anything) and you should get a nice spark when turning it over.
I would check the float bowl once just to put that to bed. If you have weak spark then check the grounds on the coil (where it physically mounts to the frame) and then check the connections in the signal wires going to the coil.
Suzuki had a problem back in about '88 with the intruders haveing poor ground on the coils and made for poor idling on those. The fix was to pull the coil and file any paint off the mount surface to fix the ground issue.
Based on the symptoms I would check gas at the bowl first. Confirm it is there. Then crank with the starter and check the plug for wet. That will tell you if you have a fuel delivery problem. If you are sure you are getting fuel all the way to the cylinder then go after the spark.
The fact it runs so well after you pull start it doesn't make sense. My gut still points back toward the petcock. Have you tried putting it on prime. let it sit for a full minute (on the clock) then try starting it. On prime if you open the float drain it should pour out until you cap it again. set to ON it should pour out and stop once you get a float bowl full.
The reason I ask is my bikes in the summer if I have to fill the bowls can take a long time cranking if I don't use the prime first. Granted those are 4 carb bikes but still a thought.
good luck
Paul
Jason wrote on 12/31/69 at 16:00:02:the plug was light white on the ends. after setting for two months i had to pull the bike about three blocks. when it set for about two days it would only take a couple of feet going about 5 mph. my big ? , there should be spark to the spark plug when i test to the head area right. the compression doesn't seem to be a problem it idles fine in the cold and has great top need. it's flat out fast off the start. i don't use the thottle when starting it. i've tried choke and no chock. never chked the fuel bowl cause i guess that if fired over when pulling that it had enough. never had a problem until i let it sat in the shed for 2 months. i got 2 suzukis so i thoyght i'd give the savage a break. now i need it back. really nice bike the dude i bought it off said he had it lowered and he also racked out the front end. i'll trie to get a pic in here some how