I disagree with other people's answer.
In general, you won't see a difference when you install a theme developped for 1.9.2.4 on 1.9.3 BUT there was some theme changes in 1.9.3 that thus, will be missing from your theme and you need to take into consideration:
app/design/frontend/base/default/layout/catalog.xml : specially with the new way Magento handles the product options (see here: https://magento.stackexchange.com/a/141375/2380)
app/design/frontend/base/default/layout/review.xml : same as above
app/design/frontend/base/default/layout/sendfriend.xml : same again
app/design/frontend/base/default/template/checkout/onepage/payment.phtml : this one is important as it affects the payment step during the checkout.
app/design/frontend/base/default/template/customer/form/edit.phtml : this one is important too as the change in 1.9.3 allows the customers to change their password
app/design/frontend/base/default/template/paypal/express/review.phtml : not 100% sure how bad it would be without the change in this file.
app/design/frontend/base/default/template/paypal/hss/js.phtml : I reckon PayPal related templates could potentially affect payments via PayPal in some way.
app/design/frontend/base/default/template/sales/guest/form.phtml : minor change
app/design/frontend/base/default/template/sales/widget/guest/form.phtml : same here
On top of that, some files in the skin folder have changed too:
skin/frontend/base/default/js/bundle.js : affects the price selection for the bundle products
skin/frontend/base/default/js/checkout/review.js : minor change
skin/frontend/base/default/js/giftmessage.js : minor change
skin/frontend/base/default/js/ie6.js : minor change
skin/frontend/base/default/js/msrp.js : minor change
skin/frontend/base/default/js/opcheckout.js : lot of changes here, which could potentially affect the checkout.
To summarize, you can install a 1.9.2.4 theme on Magento 1.9.3 but depending on how deeply customized it is, you may face issues related to the list above.
Important note
It does not affect 1.9.3.1 but in some cases, using an theme for an older Magento version will result in some security breach not being fixed and thus will make your store vulnerable to attacks.