An earth elemental digs no faster than any other creature
The only Pathfinder rules for digging that I'm aware of are part of the mundane hazard cave-ins and collapses, which says...
In 1 minute, using only her hands, a character can clear rocks and debris equal to five times her heavy load limit. The amount of loose stone that fills a 5-foot-by-5-foot area weighs 1 ton (2,000 pounds). Armed with an appropriate tool, such as a pick, crowbar, or shovel, a digger can clear loose stone twice as quickly as by hand.
(Extrapolated, a creature without tools can clear rocks and debris equal to its heavy load in 2 rounds and with tools its heavy load in 1 round. Unless, of course, your strict GM rules that a creature must labor for 1 min. to clear any debris.)
So, if the Int 4 earth elemental doesn't know how to (or can't or refuses to on religious (ahem) grounds) use a shovel, the Small earth elemental's a worse digger than the celestial pony that can be summoned using summon monster I. That is, the biped Str 16 Small earth elemental's heavy load is only 172.5 lbs., while the quadruped Str 13 Medium pony's heavy load is 225 lbs.
The example's issues
A Small earth elemental summoned by the typical level 5 wizard using summon monster II can take 5 turns to double move each turn to travel 200 ft. into the earth, but probably travels only 180 ft. into the earth after it takes a move action to attend the chest. A Small earth elemental summoned by the typical level 3 wizard using summon monster II can take 3 turns to double move each turn to travel 120 ft. into the earth, and, using tremorsense, finds the chest if the chest's within 60 ft. of the elemental, but the elemental disappears before it can return to the surface to tell the summoner what it's found, the duration of the level 3 wizard's summon monster II expiring after 3 rounds.
Were the level 5 wizard's earth elemental to have buried the chest only 100 ft. underground, the level 3 wizard's earth elemental still couldn't've retrieved the chest, but the elemental could've informed the wizard of the chest's location. (That is, the level 3 wizard's elemental takes a double move to descend 40 ft. and finds the chest as the chest's within 60 ft., then takes a double move to ascend to the surface and, in Terran, tells the wizard where the chest is, 1 round remaining on the spell summon monster II's duration.)
Keep in mind, too, that typical burrowing leaves no tunnel (therefore doubly true for the special ability earth glide), so there's no way for the earth elemental to create using its special abilities a path for the summoner to the chest.