Whether goods can be transported without issuance of Invoice

Yes. The consigner can issue a delivery challan instead of an invoice at the time of removal of goods for transportation in the following cases:
(a) supply of liquid gas where the quantity at the time of removal from the place of business of the supplier is not known,                                                                       (b) transportation of goods for job work,
(c) transportation of goods for reasons other than by way of supply, or
(d) such other supplies as may be notified by the Board.

(ICAI FAQ PUBLICATIONS 06-09-2017 TAX INVOICE, CREDIT AND DEBIT NOTES: FAQ NO. 38)

How will the transporter satisfy the proper officer, if he checks the goods in movement where no invoice is required to be raised and a delivery challan suffices

As per Rule 55 of the CGST Rules, where goods are being transported on a delivery challan in lieu of invoice. The transporter can show his delivery challan, which should inter alia, show the details of the goods, place of supply and details of the consignee.

(ICAI FAQ PUBLICATIONS 06-09-2017 TAX INVOICE, CREDIT AND DEBIT NOTES: FAQ NO. 40)