It does. India's home test season is from October to March. And it will be affected invariably if IPL is shifted to that.
Australia's second home series starts on Boxing Day. That is Dec 24. So it will run right through Jan and Feb and they will never be too happy to miss the IPL forever for that. Your suggestion of swapping the ODI series with tests is ridiculous as it is not traditional. And further, many Aussie ODI players too figure in IPL. So it makes zilch sense. Again, the First class season too runs right through that time in Australia. And considering how many Aussies play in the IPL, it will be disastrous for both Aussie players and IPL to schedule at that time.
Further, you hardly know anything about Indian weather at that time. Fog would settle in by 4.30 PM on the grounds and visibility would be terrible in Delhi, Jaipur and Bangalore. In Hyderabad, it might rain during that time. Your suggestion is both impractical and devoid of sense.
IPL is becoming qausi International. Players like Gayle have openly started supporting IPL instead of test cricket. In the coming years, it is only going to get worse. Better logic will be to find it some space during April and May.