No.

In normal daily life, Jain sādhus – including child monks (bāl‑sādhu / bāl‑muni) – are not living in a way meant to “expose their private parts” in front of people. How they dress depends on the tradition:

1. Śvetāmbara tradition

• All monks and nuns (including children) wear simple white clothes.
• Their private parts are covered at all times in public.
• Modesty (lajjā) and strict brahmacharya (complete celibacy and purity of mind and body) are essential rules.

2. Digambara tradition

• Fully initiated Digambar male monks are traditionally nude as a symbol of total renunciation.
• But:

- Bal‑muni (younger ones) are normally not taken straight into full Digambar nudity. - Before full dikshā as a nude muni, they are kept under strict guidance, with appropriate covering until they are mature enough and truly understand what they are accepting. - Even where nudity exists, it is completely a spiritual discipline, not done with any sexual or shameless intention. They avoid crowds, avoid looking at bodies, avoid any sexual talk or thought.

Important points

• Any intentional, indecent or careless exposing for sensual reasons would be a serious sin and a direct break of their mahāvrata of brahmacharya.
• Jain discipline is extremely strict:

- No sexual thoughts, no touching, no joking about such things. - Very careful about how they sit, walk, bathe, and be in public.

• If any sadhu behaved in an improper way, that would be considered against Jain dharma, not a part of it, and they can be punished by the Jain order with heavy spiritual penalties (prāyaścitta, loss of position, etc.).

So, according to Jain principles and proper practice, child sadhus are protected with modesty and strict rules of celibacy; they are not meant to casually expose their private parts in daily life.