Yes it is possible.
A a wallet is just another Dapp. A non-wlallet Dapp needs an access to an Ethereum node and then it can read blocks or transactions or write / post transactions which include data on the blockchain.
- the Dapp has to have an account on the node it does access - the smallest piece of data to write is 32bytes
- it is very expensive to write on blockchains and especially Ethereum mainnet
For even more details please check -
What a Dapp really is