Yes, it is possible to check protein expression of recombinant or cloned proteins in HTP  format only thing is you will require few special apparatus such as shaker-incubator for plates and also centrifuge for plates (to pellet down your cultures). if you arrange these requirements only thing you have to do, is to optimist conditions such as time, RPM, temperature etc as normal culturing conditions will not directly apply to plates.

HTP is common in the antibody industry using mammalian cell culture where the antibody is secreted into the culture medium and can be  assayed (robotics) in situ.  Do you expect the proteins to be secreted into the growth medium or the periplasm for E coli expression?  If the expression is soluble and intracellular then the E. coli cells need to go through a breaking procedure which may not be amenable in multi-well plates.  There's likely going to be a need for partial purification with affinity tags for the downstream bioassays depending upon what those assays are.  If the expression is insoluble then it is probably not going to be a HTP process due to solubiilization and folding steps.  

Thank you both for taking the time to post your comments.  The protein in soluble and is excreted intracellularly.  I thought about culturing them in 48-deep well plates and optimizing growth and expression.  I have all the equipment needed for culturing and expression.  We just have never done this before and was hoping there was a protocol for HTP protein expression in deep multiwell plates.  Unfortunately we are unable to tag these protein for protein purification.  We want to feed bioassay with whole expressed cells, which we know works (when cultures are grown in flasks).  I will speak to my colleagues and address your comments to them.  Thank you again for your valuable input!!! :)  Have a great day and enjoy the weekend!