Should I have one hand on the throttle during engine ignition?
Yes hand on throttle when starting, always, except on engines with fuel injection where you have to have it on the mixture because you start on idle cutoff and move it up as the engine catches.  In any case, you shouldn't be reading checklist items during the start; you just learn what to do and do it so you can be in total control.  Back to the checklist after the engine is running and you are satisfied it's running properly on its own and you can divert your attention to other things.  Whoever was telling you to hold the checklist during the start is... well... an idiot.

I don't think you'll fail a checkride, but will probably get marked down a bit for that item.  Most checkride fails are because a series of screw-ups accumulates and drops your overall score, not because of a single item, unless the single item is something critical and screwing it up is dangerous, like taxing onto a runway with an airplane on final or making a really bad judgement call or leaving out a critical item.

When you do your check ride, you will probably be convinced at the end you failed, if you made this little mistake and that little mistake, and will be shocked to hear "you passed".  Because unless you do something that shows the examiner you're dangerous, it's the overall scoring that counts.