No. As per above, only predefined wallets/blockchains types are replicated over to new sub-wallets. When you add new currencies to one sub-account, you will need to add it to your other sub-accounts in order to transfer the same asset between both sub-accounts.
If you try to transfer say Arbitrum to another sub-account that doesn’t have Artbitrum wallet, you simply need to make it your active wallet Services > Sub-Accounts > Tap the radio button next to desired account, then from the homescreen, you can now add an Arbitrum address/wallet via the toggle switch to the right of the ‘My wallets’ text, to your new active sub-account and transfer between accounts using the SEND feature, selecting the asset to send and then the Sub-Accounts tap which will list the sub-accounts you can transfer between. See also How can I transfer between sub-accounts?
NOTE: As always, you want to ensure that you triple-check token types when transacting. For example, if you’re transferring or sending USDC (ETH) you do not want to send it to USDC (SOL). In other words ensure you are matching token types: ETH > ETH, SOL > SOL, TRX > TRX. Failure to be cautious will mean you lose your asset in transfer because crypto cannot be salvaged in such examples.
Generally speaking, you don’t need to worry about making errors because sub-accounts automatically ensures all your existing wallets, blockchains and token-types are reflected in your new sub-accounts. You only need to take caution when adding new currencies/tokens to ensure compatability i.e. ERC20, BEP20, TRC20 etc.