Impossible...no. Extremely difficult and will take many years...yes, so if you decide to do it, have some patience).
There are many SP's in the set (generally if they have a tiny double digit # on front below the name then they are difficult). The only HOFer in among the rarities (unfortunately) is the Walter Johnson so that card is going to be a MAJOR stumbling block for anyone going after the set. Generally the first 30-35 cards from the set of 52 will be somewhat available if one has some patience (and isn't too picky about condition b/c these are easily broken cards) but getting those last 15-20 cards for the set will be REALLY difficult unless you happen upon a partial set or get really lucky!
-Rhett
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