Yes, one can successfully have a teacher they don't live near. Many Rinpoche's live on one coast or the other and have centers across the country, some staffed by monks/nuns, some with lay teachers. Many sangha members see their teacher once or maybe twice a year; one to one face time may be 10 minutes or less, or not at all. One reaps the benefits by making as many contacts as possible, many aspirations, much guru yoga, etc., and attending as many events where the teacher is present as possible. This often entails travel, sometimes quite extensive. You can also watch events live online, and on DVD.
Can you go it alone? Very, very tough. You can get by without a "temple" if you have a support group of some kind. Even if you have some other sangha within an hour or so, you can attend maybe once a month; that may be enough. But all alone? Everyone I know who has tried it has great difficulty. They usually end up attending some kind of local sangha, from the same school if there is one available, from a different school if not, even if just to do meditation together.
My experience has been with Vajrayana, not sure if this translates to Shingon.
Overall, I'd say doable but difficult.
Hope that helps.