I'd be inclined to say yes with the assistance of a flat reference surface or a couple of straight edges. The plane will take down high spots but is too small to find them on its own. It's certainly not the ideal way to do it.
I am fascinated that some people prefer a low angle jack plane for this. I have one but just use it on end grain, miters mostly.
I'm with Dr. Roberts that a #4 or #5 bench plane would be more useful in a basic tool kit. I find they tear out less on wavy grain, and they will plane end grain when well tuned.
I remember seeing a video about the Lee valley low angle jack plane can act as 3 planes in one if buying extra set of blades 38 and 50 degrees.
Not a cheap setup but still consider cheaper then buying 3 planes from LN or LV
You can get a flat board with a short plane, it just takes a lot more work and you need to have a straight reference surface to check your work against. Compare the piece against a straight edge, use the plane to hit the obvious high spots, rinse and repeat until the board matches the straight edge in all orientations, then take a few smoothing passes with the plane.
All that said though, for that small a piece a block plane will work just fine to get it flat enough, without any special techniques. BTDT, works just fine. Hand tool snobs will tell you you need 80 different planes to do anything, but you can get by with just 2, and this is a situation where you only need the block plane. Plenty long enough to flatten an 18 inch length, long as it isnt horribly warped out of shape
My first thought was how long do you expect to live? Sure you can do it, but you can do it with a pocket knife for that matter, but you might get kind of bored by the time you're done. As my father often said and I quote.."Wait'll you get to be my age, kid"
Turns out he was always right.
You know..there is a website called ebay where you can buy some very good old planes for 30-40 bucks. Start setting aside some money for acquisition of new and used tools.
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