Short answer - yes, do the volunteering - there's no negative side to this.

By all means tell the organization you're volunteering for that you're currently looking for a new role. Volunteers by their very nature are transitory and can stop their work at any time.

What you can do to help more is offer support to anyone following you at the time you accept a position elsewhere, in effect you're offering a handover process that will help the organization a great deal.

Volunteering can be as simple as sorting clothes at Goodwill. The task takes 5 minutes of training. Orgs like Goodwill are used to "drop in volunteers" who might show up for 2 hours and never appear again (like high schoolers doing community service for club requirements).

I think you're worried about signing up for a long-term commitment (like volunteering to help fully build a house or plan a youth camp), but you can find short term volunteer opportunities (picking up trash along a river, cleaning cages at an animal shelter) that would still get you out and be something you could talk about in a job interview.

Search for "Short term volunteer opportunities YOUR CITY". Mine has a full website with things like packing food for seniors, scanning tickets at a festival, or working at a food pantry.

It Depends on the type of Volunteer work

For the record - I work fulltime, I also volunteer in a youth organization (that has a global prescence) as a Youth Leader.

I take my volunteering very seriously - in that I dedicate an entire evening once a week to the organization, plus I spend money (technically there exists a mechanism to reimburse me for anything I spend on the kids - but Whoops! Corporate me just cannot find the Receipt...) and I also plan evenings and sometimes will invest a fair amount of my time, because I believe in the work that this organization does and I have seen some exceptionally capable young people develop leadership skills.

If that is the sort of Volunteering you are thinking of getting into - my answer would be:

NO.

It is so frustrating when we get new people in, start to train them up and suddenly they realize the hard work it takes and then dissapear. I would rather they not put their hand up in the first place.

BUT!

Not all Volunteering positions are like this - think about things like weeding around a church/communitee building/old folks home - this is the sort of thing where you can show up with 1 person or 10 and do a as much or as little as you are able to.

If this is the sort of casual/Ad-Hoc type of volunteering you are thinking of doing - then I would say go for it.

First get a feel for the market. Send out a few applications, walk by a few shops and ask. See what the feedback is.

If it turns out it's not easy, then start volunteering. Tell them you have time until you find a job.

But there is no point in volunteering when the first two burger joints are like "sure, can you start tomorrow?"

Check if there are any regulations regarding volunteer work in your jurisdiction first

In some jurisdictions, there are rules related to volunteering as a NEET, especially if you receive certain types of benefits. For example, in Flanders, those receiving unemployment benefits need to ask prior permission from the government and inform the organization that pays their benefits. I know that when I wanted to volunteer for Oxfam while unemployed I had to submit several forms for this so the government could verify that my volunteer work would not impede my job hunt. It is entirely possible that in your jurisdiction there are similar rules.