Can you have two, or three wallets synced up. Example: One on my desktop, one on my work, one on my mobile. Or would you have to send your coins to each wallet so they all have their own balances.
As this question is posed in the title it appears to be a question directed toward "hardware wallets."
As it is posed in the text it is simply "wallets," and appears to relate to software wallets. Since we don't sync hardware wallets with phones.
There are two cases of stand alone software wallets.
(A) where a seed word sequence is used by the wallet to generate all key permutations
(B) where seed words are not used in such a fashion or are not used at all
In the case of (A) you could run into issues where not all of the pieces of software are updated at exactly the same time. Note it may not be your fault; PC software updates are released but not the Android, it's delayed.
There is a further category which is "on-line wallets" such as coinbase. Here if you have logged in to the PC or the phone app everything should be the same exactly.
Also for (A) you lose the identical nature of the database if you import private keys to one of the machines and not the others. Importing keys will cause divergence.
In the case of (B) the two wallets will diverge and will not "sync."
Multiple devices likely increases risk exponentially.
