I have tickets for the SCAVI tour at the Vatican...here's my dilema. I am traveling from Cinque Terre by train, taking the earliest train I can, and will get to Rome around noon. My tickets are for 3:30 that afternoon. Do I have time to get to my hotel, checked in and then get to the Vatican? I am only in Rome a few days so I really don't want to miss this.
I don't know where your hotel is, but it it's anywhere in the city center with a taxi from the station you'll be there within 20 minutes.
If you can't check in because it's too early, just ask the hotel to hold your luggage until you come back (actually you should do that regardless to save time). Let's say another 15-20 min. for that process. From the hotel to the Vatican it varies depending on your location. If it's walking distance you can walk maybe in minutes, but otherwise you can take public transit or even a taxi. I'm sure 20-30 min. will be sufficient even in the worst case scenario. I think 1.5 hours from arrival in Rome to the tour should be sufficient for everything. Just don't stop to have lunch at a sit down restaurant, because in Italy that can take hours.
I think Roberto's right regarding the timing. Please remember that it's very warm and humid in the scavi. If it's chilly outside, wear layers of clothing that you can peel off as it gets warmer and warmer. You will go through a security checkpoint for which there may be a line. You will go around to the left (as you face St. Peter's) to get to the entrance. On my most recent visit, you cut through the left arm of Bernini's colonnade. In addition, they do not allow backpacks or any large-ish purses or bags. Don't let yourself get turned away because you have a big bag. As you face St. Peter's, to the right is a baggage check, but it has a separate security checkpoint!