Will I have to have Engine Remove to Fix Reservoir Issue?

Maybe it's the terminology that I'm not understanding here, but the "reservoir" or overflow bottle is super easy to remove or replace. But from your description I believe you are referring to the freeze plugs on the engine itself that are leaking? Freeze plugs are not designed to ever come out, but they can corrode and leak. Replacing them is always part of any engine rebuild. The problem with replacing them is getting access to them, *some* might be doable with the engine in the car, others are impossible, and the engine would have to come out. Ask the mechanic to clarify that the item he wants to replace are the freeze plugs.

I just looked at pictures of freeze plugs for the car (couldn't reach the mechanic) and those plugs are HUGE. The holes where the liquid is coming out of is the size of a screw, but it has a steady flow when it's coming out.

My 2003 Ford Taurus SES had a leak in the reservoir. The reservoir had hair line cracks in it but it had enough of them that the water would leak out. At first it was a little and then it got worse. We couldn’t tell where the water was leaking out at first but after we realized it was the reservoir my boyfriend took it off and used some opoxy glue stuff to repair the cracks. It worked for a while but still looses a little water. I am going to replace it with a new one soon. Rockauto.com has them at half the price as the local auto parts stores. The opoxy glue stuff got me through until I could afford to purchase a new one. It was not a difficult part to remove and install. We did watch a u-tube video on it first which really made it much easier. I highly recommend watching a video on any car repair before you start to be sure it is within your capability. Also it will let you know what tools you will need so you can be better prepared. Good luck. ,