No.
Supply and Distribution min size 3/4" and must be of the approved materials in the Illinois Plumbing Code. Rarely are Washing machine hoses 3/4", irrespective, not approved materials for supply or distribution for potable water Cold or Hot.
Water Heaters are not general "Plumbing Fixtures" according to the Illinois Plumbing Code.
Water Heater/s is/are a: "Plumbing Appliance": A special class of plumbing fixture intended to perform a special function. This term includes water heaters, water coolers, drinking fountains, heat exchanger and water treatment equipment other than water softeners.
The inlet is part of the Service Supply system from the Cold Water Branch Line (as in this portion of the code: "Water Heating Equpment. A shut-off valve shall be provided in the cold water branch line within 5 feet of each water storage tank or each water heater.") and the outlet is the begining of the Hot Water Distribution System.
Illinois Plumbing Code:
PART 890 ILLINOIS PLUMBING CODE : Sections Listing
See 890.1200, 890.1210, 890.1220, 890.350, 890.320 And Appendix A, Table A (scroll down approx 1/3rd way down to portions titled in bold

"Approved Materials for Water Distribution Pipe" and "Approved Materials for Water Supply" see also in same Table "Approved Standards for Plumbing Appliances/Appurtenances/Devices".
Here is a quick link to Table A of Appendix A:
http://www.ilga.gov/commission/jcar/...ZZ9996aaR.html
By the way, if that glass block behind your hand in the picture is to the outdoors the system would also not be adequately protected from freezing in NE Illinois (which is known to have sustained periods of minus 0 degrees F in the winter).