could I exchange [British coins] when I land [in LA]?
No. There's no business which provides that service there.
USA Today say
"Travelers returning from an international trip often have a handful of coins left over from their international purchases. While most foreign exchange companies and large banks are willing to buy back international bills, finding a home for unneeded coins is a bit more challenging."
They go on to suggest
- Spending them at the airport you take off from (but I doubt Dublin airport shops will accept £200 in coins in payment. Unless you kissed the Blarney stone, acquired an incredible "gift o' the gab" and are willing to overpay outrageously)
- Selling them to collectors via garage-sale or online ad (but this is after not when you land)
- Donating them to UNICEF (but donation is not exchange)
None of these meet your criteria.
Provenance & condition
One thing to be aware of is that the old-style £1 coin was forged on a large scale. At one time about 1 in 20 was a forgery. You almost certainly have one or more forged £1 coins in your £200.
If your friend was not a close friend but a recent acquaintance, or if the collection is of coins that they accumulated because the coins were refused in coin machines, you might have more than a few worthless coins in that £200.
If anyone at an airport offered to sell me £200 in coins, I'd assume it was a probably a scam and that the coins were mostly worthless.
USA Today's suggestion of selling them to collectors seems odd to me. Any serious collector of coins will want mint-condition uncirculated coins and interesting or rare coins. I doubt any of your collection fall into those categories.