It is necessary that you get access to the mailbox. This can be done with PHP. Once you have this, all you have to do is but a bulk SMS account and setup the API with your script.
If your mail provider does not give IMAP or POP3 access, you can buy a domain name for Rs. 400 per year, and hosting for 1000 per year. Bulk SMS gateway will cost you 2 or 3 K per year again.
Best is to check if you email provider is giving such features at any premium cost.
You can achieve this functionality in follow ways:
1) You need to have access to send sms using http interface, so as soon as you receive you can send alert to mobile
2) you can receive email on mobile itself and create sms in inbox, this require gprs on mobile.
3) find free sms sending script and use this on desktop to send sms on email arrival.