Yes, it can be done.

In Jain dharma:

• Snatra Puja – There is no restriction of month. It is a kalyānak‑smaran (remembrance of Tirthankar’s janma‑abhishek) and can be done on any shubh day, including in Chaitra month, in both Shwetambar and Digambar traditions.
• Gṛuh Pravesh (house entry) – Jain families usually choose a convenient, peaceful day when:

- No violence-based rituals (like havan with grains in fire, animal offerings, etc.) are done - The day begins with Navkar Mantra, Ashta‑prakari Puja or Snatra Puja, prarthana and svādhyāy - Food is strictly ahimsak, satvik, and preferably before sunset

So, doing Gruh Pravesh along with Snatra Puja in Chaitra is fully acceptable as per Jain principles. The main focus should be on bhav (inner purity), ahimsa and shuddh acharan, not on a particular month.

For more on Snatra Puja you can read here