No, you won't lose out on any Skywards Miles or benefits. This includes your sign-up and welcome spend Miles, as well as any tier upgrades you're due. They will be transferred to your account once the system update has been completed.
If you're due a Silver Tier upgrade, it will be processed after the system update and you'll be able to enjoy the benefits of it then (including an additional 12kg checked-in baggage allowance, access to the Emirates Business Class Lounge in Dubai, business class check-in and more).
You can check the Skywards Miles you've had transferred through your monthly HSBC Emirates Skywards credit card statements. Or by logging onto your Emirates Skywards account and viewing your Emirates Skywards statement.