Absolutely...Depending on how you installed the wire. Generally, when we install systems, we leave a 1' coil of extra wire per valve. This lets us strip the casing and cut just the wires we need. If you left no extra wire in the valve box, you may find it difficult to connect the ends of your wires, but it is possible. Simply run a short "jumper wire".
Remember: Both ends of your common wire must be connected to a selenoid wire. With the exception of your valves on the end of the wire, which will only have one common wire.
As for your other question, it is not neccessary to reconnect all wires after a wire splice, but it is a good idea. You only need to splice the colors that will operate a valve. However, if a zone wire ever goes bad, and they do, had you wired them all, you would have a replacement wire to use.