I found a solution to this problem.
How I found the solution ::
A). The Invoice Email template invoice_new.html has the following line :
{{layout handle="sales_email_order_invoice_items" invoice=$invoice order=$order}}
whereas the Order email template order_new.html has the following line :
{{layout handle="sales_email_order_items" order=$order}}
B). In sales.xml, layout handle 'sales_email_order_invoice_items' has a block template 'email/order/invoice/items.phtml' ... this item.phtml file has the following line ::
echo $this->getChildHtml('invoice_totals');
and sales.xml again says ::
<block type="sales/order_invoice_totals" name="invoice_totals" template="sales/order/totals.phtml">
C). Again, in sales.xml, layout handle 'sales_email_order_items' has a block template 'email/order/items.phtml' .. this item.phtml file has the following line ::
echo $this->getChildHtml('order_totals');
and sales.xml again says ::
<block type="sales/order_totals" name="order_totals" template="sales/order/totals.phtml">
D). So, both Order and Invoice emails dynamically loads "sales/order/totals.phtml" file. Now in totals.phtml file, we have a line like this ::
foreach ($this->getTotals() as $_code => $_total):
The above function getTotals() loops through the array containing Total Pricing structure including base price, shipping expenses, tax, discounts, Base price in other currencies etc.
E). As the Base Price (with BASE currency as set in Admin Panel) was coming properly in Order email, I checked the class ( from block type='sales/order_totals' ) Mage_Sales_Block_Order_Totals found in Mage/Sales/Block/Order/Totals.php. The getTotals() function is just iterating the property '$this->_totals'. I also checked how this '$this->_totals' array was created through '_initTotals()' method. In this '_initTotals()' method, $this->_totals['base_grandtotal'] has been created which is responsible for printing the Order price in Base Currency and this is what I was looking for. However, this Base price was not coming in Invoice emails. Hence I opened the Class 'Mage_Sales_Block_Order_Invoice_Totals'
F). The class 'Mage_Sales_Block_Order_Invoice_Totals' ( existing in file 'app/code/core/Mage/Sales/Block/Order/Invoice/Totals.php' ) inherits from the class 'Mage_Sales_Block_Order_Totals' and overrides the function _initTotals() which created the pricing array. However in this function, there is a line ::
$this->removeTotal('base_grandtotal');
The above line is removing the Base Price section from the _totals array. Simply commenting the line finally solved my problem.