Having recently graduated from a CompE program at the number 2 or 3 (depending on who you ask) school in my non-US country - I think it depends very much on the focus of the school's program (my alma mater, for example, is known to do much more hardware things than most CompE programs we compare ourselves to). Over the course of my four-year degree, we had four lab courses where you play hands-on with circuits and do more traditional hardware hacking (so about one every other semester).
First one is the basic breadboard class, focusing on RLC + OpAmp circuits (basically building amplifiers and Wheatstone bridges) and getting you familiar with how to use a scope, function generator, and the various other tools of the lab.
Second one is CPLDs - over the course of a semester design (in, ugh, VHDL) and build a WWII Enigma machine. Some circuit assembly (attaching various components to the main board) and DIY multiplexing, but the focus is on the CPLD.
Third one is based off a custom board with a CPLD, a little programmable TI micro-controller, and a whole lot of pins to wire-wrap things on to. My year we attached keypads, RTCs, four-line LCD displays, and speakers to do FM wavetable synth - half our final grade was dependent on how good Jingle Bells sounded when we played it back on the last day.
Fourth one was about IC design - given the schematics for several types of amplifiers we simulated them, analyzed them, and then hand-laid them out. Flash-forwards two weeks, and we got them back (as DIPs) from the fab. Rest of the course was about testing them, building a few more RLC circuits to complement and verify them, and hooking everything together to make an AM radio receiver.
If you were really into HW, there were a few electives you could take (mixed-signal analysis, IC fabrication, and a whole bunch of power engineering courses sponsored by our local utility company) that would get you more exposure to it. All of this was in addition to the on-paper analysis courses that everyone took, starting with RLC circuits and ending with the physics behind BJTs and diodes.