You might be able to detect the difference if you had intimately known a place for many years and if the program was a bit off.. maybe. Because places themselves aren't static. We know without thinking about it that just because the ocean we've been visiting every day for years smells a little more or less oceany-y one day that it is still familiar. Our brains don't expect everything to be static in a familiar environment and it seems a well done program can fool even those most familiar with the surroundings, for a while at least.
And we aren't even talking about being able to go home. We're just talking about going outside. Dump me in a holodeck outside in a place I don't know, say Montana or Bajor or Queensland and I'm going to feel happily and wonderfully outside. A native of the place might have a little comment about their being rather a lot of clover scent in the air for the time of year but I'd be none the wiser.