No, the upload page is protected by a "Captcha" - this prevents robots or spammers with automated software or such tools from automatically sending you uploads.
If you believe your website gets a lot of random traffic and your upload page link is likely to be abused, one option is to not add your upload page link to your website. Instead, add it to your email signature (see how). That way only your clients or email recipients will have your upload page address. You can change your upload page address at any time.
To make it convenient for your clients to send you secure messages easily (without login or account signup), some amount of extra messages may be acceptable - this is a choice for you. The upload page can be disabled if desired.