Essentially, yes. It is possible for the CPU to read memory at non-aligned addresses, but it takes longer. This is probably a simplification, but it works something like this:
There are generally a set of data lines that go from the RAM controller to the CPU. If you have a 64-bit processor, for example, there will be 64 lines going from the RAM controller to the CPU. The RAM controller always pulls 64 bits (8 bytes) out of RAM and sends them along the data lines to the CPU. The CPU then has to mask out what it needs and throw away the rest.
There's a catch, though. The memory controller needs to be told by the CPU which address to read from. So there are address lines that go from the CPU to the memory controller. In order to simplify the memory controller, it always reads from an 8-byte-aligned boundary. The circuitry would need to be much more complicated to read starting at any address, as I understand it (though I'm no hardware engineer).
So if you want to read memory at a non-8-byte-aligned address, the CPU sends the address of the lowest byte it needs, the memory controller masks off the 3 low bits, reads 8 bytes and sends them back to the CPU. If you crossed an 8-byte boundary, then the memory controller also needs to read the next 8-byte range and send that back. The CPU then has to mask off the right number of bytes from each read, shift them and combine them back together into 1 8-byte number. (Or perhaps that all happens in the memory controller? Either way it takes longer.)
Even if you aren't reading 8 bytes, if you read from an odd address, it still needs to mask and shift the result to put it into a register.
Some older low-end CPUs did this even for some aligned reads. For example, I believe the 8088 only had 8 data lines, so a read of 16-bits always resulted in 2 reads and twice as many cycles for memory fetches. Once the data was on the CPU, it processed as fast as the 8086, though.
As mentioned in the comments there are even some CPUs that can't do any non-aligned reads presumably to simplify their design and lower their cost.