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If we increased the size of SDRAM using the same technology, would the response time become slower? If it did become slower, would it be due to the complexity of digital logic?

Yes and no. As duDE states, memory will never run faster than the bus/clock speed driving it, but the maximum speed of memory is definitely dependent on size.

As a memory assembly gets larger, the number of levels of address decoder increase (with the log of size), and the load on the drivers increases linearly (producing roughly a logarithmic increase in delay).

So, while it is rarely worthwhile to limit the size of RAM in a off-the-shelf system in an attempt to increase speed (there are exceptions where the box adjusts clock speed based on the size of RAM), if you are a system designer, the maximum RAM size is one of the performance trade-offs you must consider.

No, it does not. As SDRAM is synchronized with the system, memory speed depends on the speed of the system. What may affect the speed of memory access is the configuration it is used in.

If your build already has a dual-channel (or triple-channel) configuration, and the increased memory does not use identical modules, then you may slow down to single-channel operation. However, this decrease is hardly noticeable, as Wikipedia says:

Tom’s Hardware found little significant difference between single-channel and dual-channel configurations in synthetic and gaming benchmarks (using a “modern (2007)” system setup). In its tests, dual-channel gave at best a 5 percent speed increase in memory-intensive tasks.

In this case, the speed may decrease, but you will experience an overall boost in performance due to the greater amount of physical memory available to your operating system. This, of course, depends on the operating system you are using and how efficient it is at utilizing the available resources.