Looking at the numbers for what is possible:
Townhall capacity 1,500
Level 40 warehouse capacity – 320,000
4 x Level 40 Warehouses capacity – 1,280,000
Level 40 Dump capacity – 1,280,000
With ambrosia you can double the warehouse/dump capacity for 1 week so the max possible storage with 4 warehouses and no dump or 1 dump and no warehouses = 2,561,500
Technically it is possible using ambrosia and 4 level 40 warehouses or 1 level 40 dump to build a level 11 palace/GR as you need 2,561,499 wood (max reductions). If you don’t plan on using ambrosia, you would need 1 level 40 dump and 4 level 40 warehouses.
For a level 10 palace/GR, you need a storage capacity of 1,410,990 (max reductions). If you plan on doing this without ambrosia – 4 warehouses alone or 1 dump alone will not be sufficient, you would need a combination of both. It comes down to whether you are planning on using ambrosia or not to achieve this - doing it without ambrosia is more difficult.
The Prof