It will fill up your storage space, but it doesn't take much memory. (And they're not the same thing - you probably have anywhere from 1 to 6 GB of memory, but a lot more than that of storage. A hard drive is still "memory", but when we say memory we're normally referring to RAM, not storage.)
Welcome to Android Central! Are you saving those photos to Keep only? I wouldn't use Keep as the only place you save photos -- save them to your Google Photos in the cloud instead.