No, this is because the timings are not compatible with one another.
The 1-Wire master (DS1481) should have a longer TW0L time because it writes to the 1-Wire slave. From looking at the DS28E07 datasheet vs the DS1481 for the TW0L timing, the TW0L timings here are equal (60 us).
If you are looking for a replacement to the DS1481 with another 1-Wire master device to handle 1-wire transactions, a good replacement candidate is the DS2484. Keep in mind this is an I2C device versus the DS1481 which was designed for use on a parallel port.