17" MacBook Pro (early 2011) 16GB RAM, 1600 MHz? Crucial and OWC both say that the 17" MacBook Pro (early 2011) supports 16 GB. But both only offer 1333 MHz when I select to buy.

Rightnow I've got a single 8GB 1600 MHz chip, have had it for years and it works fine.

Would this model have issues with two 8GB 1600 MHz chips?
Your MacBook Pro has two memory slots designed to take 204-pin PC-10600 (1333 MHz) DDR3 SO-DIMM memory chips.

Apple's official position is that this model supports up to 8GB of memory, but real world tests have proven the machine to work fine with 16GB, so both Crucial and OWC are correct in what they say.

If both of them sell the 1333MHz chips, assuming they are 204-pin PC-10600 (1333 MHz) DDR3 SO-DIMM memory chips, then these will work as they are the correct specs for your machine. Xaxxon's comment about the likely speed of what your 1600MHz chip is running at is correct. Paying for 1600MHz chips are just a waste of money.

If it was me I would go ahead and purchase two of them and install them into your computer to get the 16GB you want.

You could try just purchasing one and adding it to your machine, but you may be risking inconsistent/random performance issues having one 1600MHz chip and one 1333MHz chip installed simultaneously. 

Of course, it's up to you and you could just test this and see how you go. But, if it's cheaper to purchase the two at the same time as opposed to buying one and then another later, I'd just buy the two new 1333MHz chips. Having two identical chips is the safest option.