I would say "No", for all the reasons numb3rs said. Primarily because it is a big stretch to call them the same school. A new chapter was begun when Lewis and Glenvar joined to form Salem High in 1977. Andrew Lewis still exists in its old building as a middle school. I feel any memorabilia from its days as a high school belongs on display at the middle school. If, back in '77, they had kept the Andrew Lewis name and just moved to a new building, without adding the Glenvar people, I would agree with you. Kind of a shame, because I think there's at least one Salem High in every state of the union; there was only one Andrew Lewis. But that's all water that's long since passed under the bridge.
My brother graduated from AL, and though he has gone to plenty of Salem sporting events in the past, he has made it clear he in no way views Salem as his alma mater.
Incidentally, for two years I rented a house near the Salem Civic Center, on the ridge on Carolina Avenue. In the back yard was a depression by a tree stump that marked Lewis's original burial place. He was disinterred and reburied in East Hill sometime around the turn of the 20th century. I knew none of that when I first moved in there. My old neighbor told me, and I later read verification.
Your question raises an interesting point. What happens to all the trophies, banners, team photos, etc. from schools that just close, or are absorbed into other schools? I'm thinking of places such as Clifton Forge, that went in to Alleghany County, and Fieldale-Collinsville and Laurel Park that were absorbed by Bassett and Magna Vista, respectively. Alleghany changed their mascot from Colts to Mountaineers to honor Clifton Forge, and I think both Bassett and MV added one color from the defunct schools to their colors. But.....what becomes of all the stuff? There must be hundreds of such NOW-defunct schools around the state.
I was saddened and shocked to discover that Salem's former AD - not the esteemed Mr. King - had basically thrown out many of the trophies won in the early years of Salem High, and even some old Lewis ones. Two or three boxes of discarded trophies, many of them broken, were found just stuffed into the back of a storage space in the auxiliary gym at Salem a couple of decades ago. Most of them were then scattered on the wind, and I'm afraid that's generally what's happened to the AL memorabilia. You can probably find it on mantelpieces in a hundred different dens around the valley.
I haven't been in Salem's gym in several years, but I don't think there are even any Salem state banners hanging there anymore, are there?