Short duration corporate bond ETF

Will a "short duration investment grade corp bond" necessarily drop in price given that the rates keep ticking up over the next 5 year?

It will drop, but shorter-duration bonds drop less then longer-duration bonds (they are less sensitive to interest rates).

And in this case by how much? I have hard time wrapping my head around if such ETFs can be "overpriced" due to the past in the same way stocks might.

Does the ETF publish an "average duration"? If so, then that duration is an estimate of the percentage change in the fund as interest rates change by 1%.

So if the average duration is 4, then a 0.5% increase in interest rates would mean that the value of the bonds in the fund will drop by about 2%. (Duration, like delta for options, is not linear, but is a decent estimate for smaller changes in rates.

My goal is ultimately just the get the coupons and hope for the ETF stay unchanged.

Note that you don't necessarily get the coupons directly; the ETF will distribute funds as defined in its prospectus. What you want to look at is the yield of the fund. As far as the value of the ETF goes, look at the price history to see how volatile it is.