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This question already has an answer here:

Some commander decks have Planeswalker commanders. What happens when you put a +1/+1 counter on one of them, such as with Opal Palace?

marked as duplicate by GendoIkari, Drunk Cynic, JonTheMon, Community Feb 5 '16 at 22:33

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    Know what happens to a toad when it's struck by lightning? – Cascabel Feb 6 '16 at 1:10
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Non-creature permanents can have +1/+1 counters on them, they just don't do anything until the permanent becomes a creature. Say you have a man land. If you animate it, then add +1/+1 counters to it, they stay on it even when it stops being a creature.

Also, cards like Earthen Arms can put counters on any permanent. Its gatherer says:

Any permanent can have a +1/+1 counter put on it. Those counters won’t have any effect unless that permanent is or becomes a creature.

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A +1/+1 Counter exist on the commander. It doesn't count as a loyalty counter, it doesn't increase the loyalty.

If by some facet the commander is turned into a creature, the +1/+1 counter would change its power and toughness.

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