According to Google Finance, 45k shares change hands each day. You didn't specify how much you're buying, so I'll assume $10,000 (~400 shares). That's 1% of the daily volume according to Google Finance. I don't know if the 400 share orders fill instantly or in a few minutes.
The fund size of $400 million is roughly medium sized. Vanguard and iShares have funds with billions of assets, and small funds with $100 million in assets - it's within the middle of those ranges. So I'd think orders would fill quickly, based on the fund size.