I used to pack my tripod that way, but after my luggage and/or my tripod case failed to show up on several occasions, I stopped. Lost or delayed luggage has become an epidemic. I now only travel by carrying all of my camera equipment and my tripod (in a separate, soft case)with me on board. I have done this all over Europe and the US without difficulty. I can do without my clothes, but not my tripod. I never photograph off a tripod.
Flying within the continental USA, carrying on the tripod as a second carryon, assuming your main camera bag is first, should not be too big a problem, as most recognise what it is. This does not mean that one TSA agent won't have a specific issue. My only advice if that happens, is whatever you do, do it quietly and politely. There is a no tolerance level at some airports for "harassing" a TSA agent, and signs abound in some airports. If it is NO go, then be prepared to have another option ready.
Just flew back a couple of weeks ago from a trip to Spain via British Airways. Great carrier, and service, but they were very strict on their international flights to and from JFK, to allow one, and only one carryon. I had planned accordingly, but my family, assumed it still meant the women's purses were OK in addition. They found out the hard way, and had to reorganize their stuff and put one of each of their second bags in the checked cargo area. It all worked out OK but cost a few minutes of anguish. Luckily this was caught at ticketing and not at the gate. On a previous trip in the year to Tetons, my airplane was substituted the last minute for an RJ, regional jet, which if you do are not aware as I was, has its own very small carryon rules. I had my full Nikon D2x kit at the time and my Pelican rollon bag now became too small. I found this out going to the plane, as a agent decided to grab it from me. I wasn't about to put $10K in the cargo area. It too all worked out thanks to a great flight staff and a kind passenger who let me switch seat assignments with her, and they let me keep the case between my legs in a row that had extra room. I was very lucky, and appreciative, but it might have not turned out so well otherwise. It was then that I decided not to go through this again and plan better on the Spain trip. Happy ending had by all...