Mainly yes. Câini means dogs, unarguable. Also when is not countable, like when you talk about the whole canine race. When you talk about a very little or a very young puppy you will say cățeluș. A young dog can be called cățelandru (not much used, but with a clear meaning for all Romanians). The term cățel (which means generally ”pup”) means all of these and it can be used to refer to any dog unless that dog is very big, or very old. However, you can call a small dog cățel, even if it is old/adult dog. It is used often for a normal, familiar, cute, adult dog (as to point to familiarity, or cuteness), mostly for city dogs living in the house. In rural areas, dogs are big, they live outside (usually chained) and are called câini. Small dogs are not useful to guard the yard...
The term cățel also may refers to cloves of garlic, or (in pejorative sense) to a person than tells on others (line in gossiping).
To make it clear, you have to think deeper how diminutives are formed in Romanian. The ”-el” termination to masculine nouns is somehow equivalent to both ”small” or ”little” added in front of English nouns. The ”-uș”, or ”uț” is the same, but work for other nouns (not all masculine words have diminutives in ”-el”). Combining them you can make a diminutive of a diminutive, as in the bizarre construction ”small little doggie”. Ex: gard (fence), gărduț (small or little fence), gărduleț (same as before, or it accentuates the small size), brad/brăduț/brăduleț, pahar/păhărel/păhăruț, câine/cățel/cățelandru/cățeluș, porc/porcușor/purcel/purceluș, etc.
"-andru" is actually an augmentative suffix, used in words representing diminutives or with a reference to youth or small size. For example:
Cățelandru - young dog of a big-sized race
Copilandru - massive/tall child
Puiandru - big offspring (of human or animal); sapling
Words containing this suffix are not very common indeed.