If it's a reasonably new switch then yes as it'll have auto sensing, you can just look up the model number if you want to be 100% sure, look for 'auto MDI/MDI-X' (but as there's no uplink port, it's a pretty safe bet that it has).
Just to clarify the cross over thing...
(without auto sensing)
switch/router/hub -> host - straight
switch/router/hub -> switch/router/hub - crossover
switch/router/hub (uplink) -> switch/router/hub - straight
switch/router/hub (uplink) -> switch/router/hub (uplink) - crossover
Just remember that if you're connecting like to like then you need a crossover cable, unless at least one device has auto sensing, then it doesn't matter.
Just to clarify the cross over thing...
(without auto sensing)
switch/router/hub -> host - straight
switch/router/hub -> switch/router/hub - crossover
switch/router/hub (uplink) -> switch/router/hub - straight
switch/router/hub (uplink) -> switch/router/hub (uplink) - crossover
Just remember that if you're connecting like to like then you need a crossover cable, unless at least one device has auto sensing, then it doesn't matter.