Memory Pool Returned Memory Alignment

In my application I have a memory pool. I allocate all memory at startup in the form of a uint64 array (64 bit machine). Then construct objects in this array using placement new. So object 1 starts at position pool[1] object 2 start at position pool[2] so on so forth. Since each object will span at least 64bits or multiples of sizeof(uint64) (if it needs more uint64 slots to allocate).

Am I correct to assume that all memory returned from the pool will be aligned correctly? Since each uint64 in the array will be properly aligned by the compiler. If so, does using uint32 on a 32bit machine in the same manner will work?