Assuming that there was no-one else on base, my guess is the umpire would have to call him out. I reference rule 7.8 from the MLB rule book (link at the bottom of the post):
Any runner is out when:
(B) He intentionally interferes with a thrown ball; or hinders a fielder attempting to make a play on a batted ball
This situation falls under the first category (intentionally interfering with a thrown ball). Even though he doesn't gain an advantage, the rule does not provide an exception for that (and the comments under rule 7.8b are relevant to plays being attempted on a batted ball, and are not relevant to interference with a thrown ball).
The comments for rule 7.8b, however, do provide interesting comments on your second scenario, where "the base is no sanctuary" for a batted ball. The comments on rule 7.8b say the following:
A runner who is adjudged to have hindered a fielder who is attempting
to make a play on a batted ball is out whether it was intentional or not.
If, however, the runner has contact with a legally occupied base when he hinders the fielder, he shall not be called out unless, in the umpire’s judgment, such hindrance, whether it occurs on fair or foul territory, is intentional. If the umpire declares the hindrance intentional, the following penalty shall apply: With less than two out, the umpire shall declare both the runner and batter out. With two out, the umpire shall declare the batter out.
So if the ball was hit hard/fast enough that the player couldn't get out of the way, then it shouldn't be called intentional interference and the runner should be safe (if on a base). If the interference was intentional, then definitely out.
Rule 7.9j also says:
It is interference by a batter or runner when -
(J) He fails to avoid a fielder who is attempting to field a batted ball, or intentionally interferes with a thrown ball, provided that if two or more fielders attempt to field a batted ball, and the runner comes in contact with one or more of them, the umpire shall determine which fielder is entitled to the benefit of this rule, and shall not declare the runner out for coming in contact with a fielder other than the one the umpire determines to be entitled to field such a ball;
Again, the "intentional interference with a thrown ball" comes into play, just as in 7.8B. Rule 7.8 states the penalty for interference as:
The runner is out and the ball is dead.
So, this guy probably would have been out under the rules had he picked up the ball, even though no-one else was on and there was no advantage to be gained from it.
If the ball is called dead (or time is called - effectively the same) anyone can touch the ball. You'll often see batters pick up a ball that was fouled straight down and drops right in front of the plate, or base coaches pick up balls and toss them to the crowd or ball boy/girl for slow hit balls that have been called foul. No penalty.