Some suggest that Mark was very young- by the standards of that culture, and certainly by comparison to the other writers. I can speculate that his youthfulness (some even suggest that he was a teenager) had something to do with his style as it pertains to the heavy use of the adverb. Also, the theory you mentioned seems quite valid, for even John was known for using the language to specifically motivate- every time John uses the word "believe," he uses the verb form, because his gospel seems to be aimed at getting people to come to the conclusion that Jesus is the Son of God and to ACT on that belief. Mark's gospel could have a very similar immediacy.
Interestingly enough, the root word euthy actually has another meaning that may highlight the intent of the word, as it certainly pertains to Christ: it means to do things properly and without allowing for detours, "straight from point A to God's point B." (Strong's).
Also keep in mind that ultimately all writers in the NT (and OT) are subject to the Holy Spirit. Any urgency we detect is God encouraging us not to delay, any expediance we notice is meant to be noticed.
Beyond that, we have no hardcore proof of Mark's motives, but we can rightly conclude that when someone says the word "immediately," they want you to take notice of the timeliness and swiftness by which something is done.