Yes it is possible. Budgets have been changed in Odoo 17.4 and we longer need dates on budget lines or budgetary positions. We can allocate budgets and track them on project following these steps:

1. Let's assume we have a project for Pepsi.
2. I will create two Budgets; one for expenses and one for Revenue and assign them to Project Pepsi:

3. At this point because the Budgets are not open yet, they will not be reflected on the Project Updates yet:

4. After I open both Budgets they will start to reflect on the Project Updates:

5. I will create an Invoice and a bill, hit the analytic account of the Project Pepsi and see how it will be reflected on the project's budget and on the revenue budget:

6. If an invoice or a bill is in draft state and hasn't been posted, it won't affect the project's budget but it will show in the project's profitability under the To Invoice:

7. After you're done with the budget you can mark it as done: