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DHCP- query

please suggest on the below mentioned scenario ,

currently The network connectivity as fallows 

                                              1) connectivity   ROUTER--- > L3 switch -- host machine 

                                              2) On  L3 switch  DHCP pool configured , all desktop connected to same switch

                                              2) Router and L3 connected  via OSPF dynamic routing protocol

                                              3) Gate way for the  desktop is switch  VLAN  10 configured with IP 10.10.x.1 /24

changes  :

             1) Need  to move  desktop gateway ( 10.10.x.1) on the router LAN interface insted of Switch vlan 10.

             2) the connectivity between router and Switch will be L2  ,

             3) DHCP pool will be on the switch  only  , not on the router

             4)  default route  will be configured on the switch towards router LAN interface  ( 10.10.x.1/24)

In this scenario is DHCP works ( configuration  mentioned below ) ??  .

On  DHCP  configuration  "default-router 10.10.x.1 "    for the DHCP scope .    10.10.x.1/24 currently on the switch

the  desktop gateway address 10.10.x.1 will be moved to router LAN interface  . 

Is  host machine  will  install  gate way address ( through DHCP pool  ) and able reach the gateway  10.10.x.1  ( router)

I think it should work since  till router LAN interface  its broadcast domain .   please suggest  .

Existing Switch configuration :

ip dhcp pool test

   network 10.10.x.0


   default-router 10.10.x.1


   lease 5


ip dhcp excluded-address 10.10.x.1 10.10.x.50

Interface vlan 10

ip address 10.10.x.1

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