Does the Aspect of the Moon Eldritch Invocation effectively allow for unending Wild Shape?

Question

Let's assume minimum, Moon Druid 4, Pact of the Tome Warlock 3

Wild Shape works by:

You can stay in a beast shape for a number of hours equal to half your druid level (rounded down). You then revert to your normal form unless you expend another use of this feature. You can revert to your normal form earlier by using a bonus action on your turn. You automatically revert if you fall unconscious, drop to 0 hit points, or die.

With level 4 Moon Druid, the PC has 2 hours of wild shape time without expending another use. Moon subclass lets them use only a bonus action to expend a use of wild shape. And a short rest is only an hour. So I am thinking that taking a bonus action every other hour of resting would help here.

Aspect of the Moon is:

You no longer need to sleep and can't be forced to sleep by any means. To gain the benefits of a long rest, you can spend all 8 hours doing light activity, such as reading your Book of Shadows and keeping watch.

Could the druid spend their week of down time in town wild shaped the whole time, and could the same druid stay in a tiny form like a house cat and be carried by the party to stay in wild shape indefinitely until strenuous activity or being dropped to 0 hp occur?

Answer 1

Only after 8 levels of Druid.

If you follow XGtE's optional rules, you still need long rests, even if you don't sleep.

Whenever you end a 24-hour period without finishing a long rest, you must succeed on a DC 10 Constitution saving throw or suffer one level of exhaustion.

So you have to take long rests over your week or risk exhaustion. To maintain a week-long beast shape, you can short rest while Wild Shaped, to recover Wild Shape uses and maintain your transformation. However, long and short rests are mutually exclusive, as per this question, so you need to use both Wild Shape uses during a long rest.

This is fine, since the transformation isn't enough to interrupt the rest.

If the rest is interrupted by a period of strenuous activity - at least 1 hour of walking, fighting, casting spells, or similar adventuring activity - the characters must begin the rest again to gain any benefit from it.

But, in order to be able to use both Wild Shapes to accommodate a single long rest, you must be at least a level 8 Druid, so that each Wild Shape lasts 4 hours.

Answer 2

Use of short and long rests during downtime is up to the DM

There is nothing specific in the rules about whether the 'time' during downtime includes short rest and long rest mechanics, so it's really up to the DM whether or not those are active during the downtime activities that are being pursued.

If the DM rules that this is possible, then BlueMoon93's answer covers the mechanical requirements and impacts for trying this.

If they rule it isn't possible, then the plan won't work at all.