They can, but there's no point. You will be required to treat everything they pay you as income, and justify any expenses (mileage, etc.) that you deduct from that income before calculating how much tax you owe.
You should also consider that you will have to pay self-employment tax (Social Security and Medicare) of approximately 12.9% on the result of schedule C (income less allowable expenses) as well as income tax on your total taxable income (SE income less half SE tax to match the exclusion of employer half FICA for W2 people, plus any investment income or realized gain, pre-2019 alimony, most disability or retirement benefits if you get those, damages from a lawsuit other than injury, etc., less applicable deductions and credits). [thanks dave_thompson_085]
The irs.gov website is quite helpful in telling you what allowances you can claim with or without receipts, but it's probably worth consulting with an accountant.