Why would he get the throne? I mean he would be behind Elizabeth I's children.
OOC: OP specified that Arabella (presumably Lady Arabella Stuart, one of the three major possible rival claimants to James) succeeded Elizabeth.
IC: Arabella I was Elizabeth's first cousin twice removed, not her daughter. Elizabeth I didn't have any children. I think you must be thinking of Elizabeth II and Arabella II, in the late 17th century.
I really don't see how James VI would get the English throne. Under English law at the time, foreigners couldn't inherit English titles. Besides which, England had just gotten done fighting a long war to resist Spanish domination: why would they then simply roll over for Scotland? Even if Arabella were to have some sort of falling out with Elizabeth, there were plenty of other English claimants. The Seymours and the Stanleys both had better legal claims even than Arabella until the Third Act of Succession was repealed in Arabella's favor, plus there were the rumors that Lord Hunsdon was a bastard son of Henry VIII.