Yes indeed you can experience every class and job with just one character, (many including myself have already done that and got all our jobs to lv.50, etc) It takes time to do that of course but if that's what you want to do it is possible

Each job has it's own allocation of stats, so it doesn't matter what you spec for LNC/DRG as that wont affect any other class/job. (of course the exception is SMN/SCH as mentioned by Duude007).

Hope that helps