As others have mentioned, the conventional answer is 'no'.
However, here is one interesting angle of the new cryptocurrency trading market to me - it operates 24/7/365 (yes even Christmas day!). Now I'm told that the biggest markets are the US and Korea, so perhaps, given sufficient liquidity, we could back out a USDKRW rate over the weekend given the USD and KRW spot rates for a given digital asset?
The futures markets are more liquid than the cash, but as the margin requirements need to be posted in spot, that should guarantee some transaction quantity round-the-clock.

Here is the futures exchange at binance.com ticking away very happily on Saturday morning
And here is a python snippet (provided caveat emptor!) that will pull the most recent BTC-USD and BTC-EUR trades from coinbase, and calculate the approximate rate for EURUSD any time - weekend not a problem! You will need to pip install cbpro
first:
import cbpro
public_client = cbpro.PublicClient()
for x in public_client.get_product_trades(product_id='BTC-USD'):
last_USD = x
print("Dollar last trade time: {}".format(last_USD['time']))
break
for x in public_client.get_product_trades(product_id='BTC-EUR'):
last_EUR = x
print("Euro last trade time: {}".format(last_EUR['time']))
break
float(last_USD['price']) / float(last_EUR['price'])
Which gives:
