Soundstage? Sure. Speaker/room interaction (along with the original recording) is the key factor in soundstage, so the key question is, how well does the recorder preserve the locational information on the original recording? Good reel-to-reel certainly will. Cassette's a bit dicier, since you certainly lose something with the inevitable dynamic compression.
If you're thinking more generally about "that vinyl sound," yes, a good recorder will capture that--just as it captures all the pops and clicks. :)
If you're thinking more generally about "that vinyl sound," yes, a good recorder will capture that--just as it captures all the pops and clicks. :)